Physical Review D最新文献

{"title":"Euclidean AdS wormholes and gravitational instantons in the Einstein-Skyrme theory","authors":"Fabrizio Canfora, Cristóbal Corral, Borja Diez","doi":"10.1103/physrevd.111.084072","DOIUrl":"https://doi.org/10.1103/physrevd.111.084072","url":null,"abstract":"Euclidean anti–de Sitter (AdS) wormholes provide a natural setup for studying the anti–de Sitter/conformal field theory (AdS/CFT) correspondence with multiple boundaries. However, from a bottom-up perspective, they cannot be embedded in the four-dimensional Einstein-AdS-Maxwell theory if these boundaries have positive curvature. Nevertheless, Maldacena and Maoz showed that this obstruction could be circumvented by introducing merons in the four-dimensional Einstein-AdS-Yang-Mills theory. In this work, we show that Euclidean-AdS wormholes also exist in the four-dimensional Einstein-AdS-Skyrme theory, whose matter sector possesses a nontrivial baryonic charge. We compute its free energy and show that it does not depend on the integration constants whatsoever, resembling topological solitons. Additionally, we obtain its holographic stress tensor and show that it vanishes, allowing us to interpret this configuration as a holographic Bogomol’nyi-Prasad-Sommerfield (BPS) state. Other topologically nontrivial ground states in Einstein-Skyrme theory are found, such as gravitational instantons, representing the homotopically inequivalent vacua of the theory. We find that they develop Hawking-Page phase transitions above a critical temperature. Some of these solutions are periodic in Euclidean time, representing the gravitational analog of calorons in Yang-Mills theory. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"9 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143884785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Constraining the superheavy dark matter origin of ultrahigh-energy cosmic rays with the Amaterasu event","authors":"Prantik Sarmah, Nayan Das, Debasish Borah, Sovan Chakraborty, Poonam Mehta","doi":"10.1103/physrevd.111.083048","DOIUrl":"https://doi.org/10.1103/physrevd.111.083048","url":null,"abstract":"Amaterasu, the second most energetic (244 EeV) cosmic ray particle has been recently detected by the Telescope Array (TA) surface detector. The origin of the TA Amaterasu event is puzzling, as its arrival direction points back to a void in the local Universe, lacking conventional astrophysical ultrahigh-energy (UHE) cosmic ray sources. Hence, we explore the possibility if this TA Amaterasu event could have originated from the decay of superheavy dark matter (SHDM) in the Milky Way. Such an origin also opens up multimessenger detection channels in both UHE gamma rays and UHE neutrinos. In this present work, using the TA Amaterasu event and the multimessenger limits/sensitivities from various UHE telescopes, we place stringent constraints on the lifetime and mass of the SHDM. We find that the nondetection of the corresponding gamma rays at the Pierre Auger Observatory (PAO) and the TA is in severe tension with the SHDM parameter space required to explain the TA Amaterasu event. Additionally, we extend the multimessenger analysis to the future UHE gamma-ray and UHE neutrino telescopes such as PAO upgrade, GRAND 200k, and IceCube-Gen2. We find that the bounds from the future neutrino telescopes will be able to compete with the present UHECR bounds. However, compared to the existing UHE gamma-ray bounds, the future PAO upgrade and the GRAND 200k gamma-ray detectors will improve the bounds on SHDM lifetime by at least one order of magnitude. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"71 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143884908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermoelectric effects of an interacting hadron gas in the presence of an external magnetic field","authors":"Kamaljeet Singh, Kshitish Kumar Pradhan, Dushmanta Sahu, Raghunath Sahoo","doi":"10.1103/physrevd.111.074033","DOIUrl":"https://doi.org/10.1103/physrevd.111.074033","url":null,"abstract":"The hot and dense hadronic medium formed during the heavy-ion collisions at the Relativistic Heavy Ion Collider and Large Hadron Collider energies can show thermoelectric effects in the presence of temperature gradients and nonzero baryon chemical potential. In this article, we study the thermoelectric coefficients of an interacting hot and dense hadron gas using the relativistic Boltzmann transport equation under the relaxation time approximation. We discuss the thermoelectric properties within different frameworks of hadron resonance gas models. In the presence of an external magnetic field, the thermoelectric coefficients become anisotropic, which leads to Hall-like thermoelectric coefficients, namely Nernst coefficients, along with the magneto-Seebeck coefficients. For the first time, we also estimate the Thomson coefficient of the medium, which comes into the picture due to the temperature dependence of the Seebeck coefficient of the medium. In the context of studying the thermoelectric generator performance, we calculate the values of the thermoelectric figure of merit of the medium. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"8 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143884910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: Hilbert space of a trivalent vertex","authors":"Saurabh V. Kadam, Aahiri Naskar, Indrakshi Raychowdhury, Jesse R. Stryker","doi":"10.1103/physrevd.111.074516","DOIUrl":"https://doi.org/10.1103/physrevd.111.074516","url":null,"abstract":"The construction of gauge-invariant states of SU(3) lattice gauge theories has garnered new interest in recent years, but implementing them is complicated by the need for SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron (LSH) approach to lattice gauge theories, the elementary excitations are strictly gauge invariant, and constructing the basis requires no knowledge of Clebsch-Gordon coefficients. Originally developed for SU(2), the LSH formulation was recently generalized to SU(3), but limited to one spatial dimension. In this work, we generalize the LSH approach to constructing the basis of SU(3) gauge-invariant states at a trivalent vertex—the essential building block to multidimensional space. A direct generalization from the SU(2) vertex yields a legitimate basis; however, in certain sectors of the Hilbert space, the naive LSH basis vectors so defined suffer from being nonorthogonal. The issues with orthogonality are directly related to the “missing label” or “outer multiplicity” problem associated with SU(3) tensor products and may also be phrased in terms of Littlewood-Richardson coefficients or the need for a “seventh Casimir” operator. The states that are unaffected by the problem are orthonormalized in closed form. For the sectors that are afflicted, we discuss the nonorthogonal bases and their orthogonalization. A few candidates for seventh Casimir operators are readily constructed from the suite of LSH gauge-singlet operators. The diagonalization of a seventh Casimir represents one prescriptive solution toward obtaining a complete orthonormal basis, but a closed-form general solution remains to be found. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"45 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143884913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"From noncommutative Yang-Mills theory to noncommutative gravity through a classical double copy map","authors":"Larisa Jonke, Eric Lescano","doi":"10.1103/physrevd.111.086031","DOIUrl":"https://doi.org/10.1103/physrevd.111.086031","url":null,"abstract":"We compute the first nontrivial noncommutative correction to the Einstein-Hilbert Lagrangian, which arises from the double copy of noncommutative Yang-Mills theory (ncYM). We start by considering linear and quadratic θ</a:mi></a:math>-corrections up to cubic order in fields in ncYM theory and in arbitrary <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mi>D</c:mi></c:math> dimensions. We compute the first nontrivial corrections to the three-points vertex operators and use them to construct a double copy theory of the form ncYM <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:mo>×</e:mo></e:math> ncYM. The resulting theory is given by a double geometrical formalism which includes noncommutative corrections to the perturbative cubic double field theory (DFT) formulation, where the star product of the theory is doubled in agreement with the doubling of the physical coordinates of the theory. Upon solving the level matching condition the noncommutative products are identified and they produced <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><g:msup><g:mi>θ</g:mi><g:mn>2</g:mn></g:msup></g:math>-corrections to the cubic DFT action. We analyze the pure gravitational limit of this formulation considering <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><i:mi>D</i:mi><i:mo>=</i:mo><i:mn>4</i:mn></i:math> and imposing the transverse-traceless gauge. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"50 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143884801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stepping up superradiance constraints on axions","authors":"Samuel J. Witte, Andrew Mummery","doi":"10.1103/physrevd.111.083044","DOIUrl":"https://doi.org/10.1103/physrevd.111.083044","url":null,"abstract":"Light feebly-coupled bosonic particles can efficiently extract the rotational energy of rapidly spinning black holes on subastrophysical timescales via a phenomenon known as black hole superradiance. In the case of light axions, the feeble self-interactions of these particles can lead to a nonlinear coupled evolution of many superradiant quasibound states, dramatically altering the rate at which the black hole is spun down. In this work, we extend the study of axion superradiance to higher order states, solving for the first time the coupled evolution of all states with n</a:mi>≤</a:mo>5</a:mn></a:math> in the fully relativistic limit (with <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mi>n</c:mi></c:math> being the principal quantum number). Using a Bayesian framework, we rederive constraints on axions using the inferred spins of solar mass black holes, demonstrating that previously adopted limit-setting procedures have underestimated current sensitivity to the axion decay constant <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:msub><e:mi>f</e:mi><e:mi>a</e:mi></e:msub></e:math> by around 1 order of magnitude and that the inclusion to higher order states allows one to reasonably capture the evolution of typical high-spin black holes across a much wider range of parameter space, thereby allowing constraints to be extended to more massive axions. We conclude with an extensive discussion on the systematics associated with spin inference from x-ray observations. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"130 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gravitational form factor D of charmonium from shear stress","authors":"Tianyang Hu, Xianghui Cao, Siqi Xu, Yang Li, Xingbo Zhao, James P. Vary","doi":"10.1103/physrevd.111.074031","DOIUrl":"https://doi.org/10.1103/physrevd.111.074031","url":null,"abstract":"Based on our recent analysis of the hadronic matrix element of the stress-energy tensor in covariant light-front dynamics, we extract the charmonium gravitational form factor D</a:mi>(</a:mo>Q</a:mi>2</a:mn></a:msup>)</a:mo></a:math> from shear stress <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:msup><e:mi>T</e:mi><e:mn>12</e:mn></e:msup></e:math>. This is in contrast to our recent work using the (light-front) energy density <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><g:msup><g:mi>T</g:mi><g:mrow><g:mo>+</g:mo><g:mo>−</g:mo></g:mrow></g:msup></g:math>. Indeed, by comparing these two currents, we identify terms that are responsible for the violation of the current conservation. Numerical results based on basis light-front quantization show that the violation effects are small, and the <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><i:mi>D</i:mi></i:math> term extracted from the two currents are close to each other, hence validating our previous work using <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><k:msup><k:mi>T</k:mi><k:mrow><k:mo>+</k:mo><k:mo>−</k:mo></k:mrow></k:msup></k:math>. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"44 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Viscous accretion and ejection from tori around black holes in general relativity","authors":"Masaru Shibata, Kyohei Kawaguchi, Alan Tsz-Lok Lam","doi":"10.1103/physrevd.111.083042","DOIUrl":"https://doi.org/10.1103/physrevd.111.083042","url":null,"abstract":"We systematically perform long-term (millions of Schwarzschild time) axisymmetric viscous hydrodynamics simulations for tori around black holes in general relativity supposing the super-Eddington accretion flow. The initial condition for the tori is modeled simply by the Fishbone-Moncrief torus with a constant specific angular momentum j</a:mi></a:math> but with a wide variety of <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mi>j</c:mi></c:math>. Such a torus may be a remnant after tidal disruption of ordinary stars near a relatively low-mass supermassive black hole or an outcome of an inflow of the matter with a low specific angular momentum. We find that, for a given density profile, the fraction of the mass infall onto the black hole is approximately proportional to <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:msup><e:mi>j</e:mi><e:mrow><e:mo>−</e:mo><e:mn>1</e:mn></e:mrow></e:msup></e:math>, indicating that only a minor fraction of the matter in the torus formed far from the black hole falls into the black hole, while the majority is ejected with the typical average velocity of a few percent of the speed of light. We also find that the mass ejection is driven only outside <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><g:mrow><g:mo>≈</g:mo><g:mn>2</g:mn><g:msub><g:mrow><g:mi>r</g:mi></g:mrow><g:mrow><g:mi>ISCO</g:mi></g:mrow></g:msub></g:mrow></g:math>, where <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><i:msub><i:mi>r</i:mi><i:mrow><i:mi>ISCO</i:mi></i:mrow></i:msub></i:math> is the areal radius of the innermost stable circular orbit around black holes, which depends strongly on the black hole spin. We derive an approximate fitting formula for the spin dependence on the mass infall fraction as <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><k:mrow><k:mo>∝</k:mo><k:msubsup><k:mrow><k:mi>r</k:mi></k:mrow><k:mrow><k:mi>ISCO</k:mi></k:mrow><k:mrow><k:mn>0.7</k:mn></k:mrow></k:msubsup></k:mrow></k:math>, which suggests that the rapid growth of supermassive black holes proceeded primarily by the accretion of the matter with the angular momentum counterrotating with the black hole spin. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"3 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized symmetry constraints on deformed 4D SCFTs","authors":"Monica Jinwoo Kang, Craig Lawrie, Ki-Hong Lee, Jaewon Song","doi":"10.1103/physrevd.111.086028","DOIUrl":"https://doi.org/10.1103/physrevd.111.086028","url":null,"abstract":"We explore the consequence of generalized symmetries in four-dimensional N</a:mi>=</a:mo>1</a:mn></a:mrow></a:math> superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the Adler-Bell-Jackiw (ABJ) anomaly, we find that many of these theories have mixed zero-form or one-form ’t Hooft anomalies. Then we classify the relevant deformations of these SCFTs that preserve the anomaly. From this mixed anomaly together with the anomalies of the discrete zero-form symmetries, we find obstructions for the relevant deformations of these SCFTs to flow to a trivially gapped phase. We also study non-Lagrangian SCFTs formed by gauging copies of Argyres-Douglas theories and constrain their deformations. In particular, we explore a new duality between the diagonal gauging of two <d:math xmlns:d=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><d:msub><d:mi mathvariant=\"script\">D</d:mi><d:mn>3</d:mn></d:msub><d:mo stretchy=\"false\">(</d:mo><d:mi>S</d:mi><d:mi>U</d:mi><d:mo stretchy=\"false\">(</d:mo><d:mi>N</d:mi><d:mo stretchy=\"false\">)</d:mo><d:mo stretchy=\"false\">)</d:mo></d:math> theories and <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><k:mi>S</k:mi><k:mi>U</k:mi><k:mo stretchy=\"false\">(</k:mo><k:mi>N</k:mi><k:mo stretchy=\"false\">)</k:mo></k:math> gauge theory with two adjoints. We also repeat our analysis for a host of nonsupersymmetric gauge theories having nontrivial one-form symmetry including examples that appear to flow to Bank-Zaks type CFTs. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"12 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New tool to detect inhomogeneous chiral-symmetry breaking","authors":"Theo F. Motta, Julian Bernhardt, Michael Buballa, Christian S. Fischer","doi":"10.1103/physrevd.111.074030","DOIUrl":"https://doi.org/10.1103/physrevd.111.074030","url":null,"abstract":"In this paper, we discuss a novel method to search for inhomogeneous chiral symmetry breaking in theories with fermions. The prime application we have in mind is QCD, but the method is also applicable for other theories, including solid state applications. It is based on an extension of the chiral susceptibility to inhomogeneous phases, and it works as a stability analysis. Our method allows us to determine when homogeneous solutions have the tendency to create spatially modulated condensates. As proof of principle, we apply this technique to a rainbow-ladder QCD model and find that its phase diagram contains an inhomogeneous region. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"17 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143872889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}