Letters in Mathematical Physics最新文献

{"title":"A complex geometric perspective on the a, c anomalies","authors":"Brian R. Williams","doi":"10.1007/s11005-026-02110-7","DOIUrl":"10.1007/s11005-026-02110-7","url":null,"abstract":"<div><p>The <i>a</i>, <i>c</i> anomalies are well-known invariants of a four-dimensional conformal field theory. Like the standard Weyl anomaly, they appear as coefficients of the trace anomaly of the energy-momentum tensor. In *super*conformal field theories, <i>R</i>-symmetry and conformal symmetry are intertwined and hence <i>a</i>, <i>c</i> anomalies can often be expressed in terms of mixed gravitational-<i>R</i>-symmetry anomalies. This paper studies the holomorphic twist of four-dimensional superconformal field theories and relates the famous <i>a</i>, <i>c</i> anomalies to complex geometric invariants of the twisted theory.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Low-energy resolvent estimates for slowly decaying attractive potentials","authors":"Kenichi Ito,&nbsp;Tomoya Tagawa","doi":"10.1007/s11005-026-02123-2","DOIUrl":"10.1007/s11005-026-02123-2","url":null,"abstract":"<div><p>We discuss the low-energy resolvent estimates for the Schrödinger operator with slowly decaying attractive potential. The main results are Rellich’s theorem, the limiting absorption principle and Sommerfeld’s uniqueness theorem. For the proofs, we employ an elementary commutator method due to Ito–Skibsted, for which neither of microlocal or functional analytic techniques is required.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Algebraic Leonard trio approach to rational functions: the Hahn case","authors":"Nicolas Crampé,&nbsp;Quentin Labriet,&nbsp;Lucia Morey,&nbsp;Luc Vinet","doi":"10.1007/s11005-026-02122-3","DOIUrl":"10.1007/s11005-026-02122-3","url":null,"abstract":"<div><p>The finite families of Hahn polynomials and associated biorthogonal rational functions are interpreted algebraically in the framework of Leonard trios. We introduce the trio Hahn algebra and prove that it is isomorphic to the meta Hahn algebra, thereby clarifying the structural connection between Leonard trios and meta algebras. Finite-dimensional realizations in terms of difference operators are constructed, and the functions of interest arise as overlaps between eigensolutions of ordinary eigenvalue problems. Their bispectral and biorthogonality properties follow naturally from the algebraic framework. \u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Spatial localization of relativistic quantum systems: the commutativity requirement and the locality principle—part II: a model from local QFT","authors":"Valter Moretti","doi":"10.1007/s11005-026-02120-5","DOIUrl":"10.1007/s11005-026-02120-5","url":null,"abstract":"<div><p>This paper is the second and final part of a two-part study. We construct a class of positive-energy relativistic spatial localization observables in Minkowski spacetime within the standard framework of quantum field theory, based on the stress–energy–momentum tensor smeared with suitable test functions. For each fixed timelike direction, the construction yields a family of positive operator-valued measures (POVMs) defined on spacelike hypersurfaces, which are well defined on each <i>n</i>-particle sector and satisfy a natural relativistic causality condition ruling out superluminal propagation of detection probabilities. The proposed localization observables arise from local or quasi-local quantum-field-theoretic quantities, thereby providing a rigorous realization of previously heuristic constructions. In the one-particle sector, the scheme reduces to the observable introduced by the author in previous literature, and its first moment reproduces the Newton–Wigner position operator under suitable normalization and centering conditions. Since the Reeh–Schlieder theorem implies that the normally ordered stress–energy–momentum tensor need not be positive on the full Fock space, we analyze the role of quantum energy inequalities and establish lower bounds that allow us to control deviations from positivity. This leads to the introduction of regularized families of operators, bounded from below, that approximate the localization effects. We further construct conditional localization observables associated with finite laboratories by means of suitably modified local energy operators. In particular, by Haag duality, the resulting conditional POVMs are shown to belong to local von Neumann algebras and hence to commute when associated with causally separated regions, in agreement with the Araki–Haag–Kastler framework. Our results provide a quantum-field-theoretic implementation of the idea that commutativity of localization observables should be recovered at the level of conditional measurements in spacetime regions of finite extent.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02120-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On support cardinality for the discrete Schrödinger equation","authors":"Linjun Li","doi":"10.1007/s11005-026-02124-1","DOIUrl":"10.1007/s11005-026-02124-1","url":null,"abstract":"<div><p>How sparse can a nontrivial solution of a discrete Schrödinger equation be? In this note, we study Dirichlet solutions on a finite <i>d</i>-dimensional lattice box, allowing an arbitrary real potential, and measure sparsity by the number of lattice sites at which the solution is nonzero (assuming it is nonzero at the origin). Our main result is a dimension-reduction principle: the minimal possible support size cannot decrease when the dimension increases. Consequently, any lower bound proved in dimension <span>(d-1)</span> automatically yields the same lower bound in dimension <i>d</i>. As an application, we obtain a nearly sharp lower bound in four dimensions, matching the best known two-dimensional constructions up to a logarithmic factor.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"A T-fold black hole in doubled type IIB","authors":"Mir Faizal,&nbsp;Arshid Shabir","doi":"10.1007/s11005-026-02105-4","DOIUrl":"10.1007/s11005-026-02105-4","url":null,"abstract":"<div><p>We construct an asymptotically flat T-fold representative of a four-dimensional dyonic black-hole charge orbit in doubled type-IIB theory. Starting from the F1-P-NS5-KKM toroidal seed, an integral parabolic T-duality monodromy is imposed on an active doubled three-torus. The non-geometric data enter only through this global patching: the Reissner–Nordstrom-type term is sourced by conserved four-dimensional electric and magnetic field strengths in the doubled Kaluza–Klein/winding local system, not by an internal algebraic <span>(Q)</span>-flux alone. Exact duality preserves the local equations, the BPS index and the <span>(O(6,6))</span>-invariant of the NS–NS/<span>(N=4)</span> charge sublattice governing the entropy. The minimal Einstein–Maxwell dilaton slice contains a running scalar branch and an equal-charge Reissner–Nordstrom limit; the extremal near-horizon region is locally <span>(textrm{AdS}_2times S^2)</span>, with the compact factor globally T-duality patched.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Dyson expansion for form-bounded perturbations and applications to the polaron problem","authors":"Davide Desio,&nbsp;Robert Seiringer","doi":"10.1007/s11005-026-02107-2","DOIUrl":"10.1007/s11005-026-02107-2","url":null,"abstract":"<div><p>We present an abstract Dyson expansion for perturbations that are merely relatively form-bounded, and apply it to the polaron problem. For a large class of polaron-type models, including the Fröhlich and Nelson models, we prove that the vacuum expectation value of the heat semi-group is a completely monotone function of the square of the total momentum. Consequently, the ground-state energy is a concave function of the square of the momentum, a result recently proved for the Fröhlich model in [14] using a probabilistic approach via Wiener integrals.\u0000\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02107-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the boundary Carrollian conformal algebra","authors":"Lucas Buzaglo,&nbsp;Xiao He,&nbsp;Tuan Anh Pham,&nbsp;Haijun Tan,&nbsp;Girish S. Vishwa,&nbsp;Kaiming Zhao","doi":"10.1007/s11005-026-02118-z","DOIUrl":"10.1007/s11005-026-02118-z","url":null,"abstract":"<div><p>We initiate the mathematical study of the boundary Carrollian conformal algebra (BCCA), an infinite-dimensional Lie algebra recently discovered in the context of Carrollian physics. The BCCA is an intriguing object from both physical and mathematical perspectives, since it is a filtered but not graded Lie algebra. In this paper, we first construct some modules for the BCCA and one of its subalgebras, which we call <span>(mathcal {O})</span>, by restriction of well-known modules of the BMS₃ and Witt algebras, respectively. Along the way, we prove the irreducibility criteria for the so-called induced modules of the BMS₃ algebra (which we prefer to call massive modules to avoid ambiguity) and show that this is the same criteria for the irreducibility of the Verma modules of the BMS₃ algebra. Interestingly, the modules generated by the action of the BCCA on the generating vector of the massive modules are also irreducible under the same criteria. When these criteria hold, every massive module decomposes into a direct sum of two BCCA-submodules, each of which we conjecture to be indecomposable. Meanwhile, restricting Verma modules to the BCCA and <span>(mathcal {O})</span> leads to free or “almost-free” modules, which are not particularly interesting from a representation-theoretic viewpoint. This motivates the construction of BCCA modules intrinsically. To do this, we go through some structure theory on the BCCA to define a new basis and a decreasing filtration on the algebra, using which we construct Whittaker modules over the BCCA and the subalgebra <span>(mathcal {O})</span> and prove criteria for their irreducibility.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02118-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction to: New model category structures for algebraic quantum field theory","authors":"Victor Carmona","doi":"10.1007/s11005-026-02114-3","DOIUrl":"10.1007/s11005-026-02114-3","url":null,"abstract":"","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Riemann–Hilbert approach for the nonlocal modified Korteweg–de Vries equation with a step-like oscillating background","authors":"Yan Rybalko","doi":"10.1007/s11005-026-02119-y","DOIUrl":"10.1007/s11005-026-02119-y","url":null,"abstract":"<div><p>This work focuses on the Cauchy problem for the nonlocal modified Korteweg–de Vries equation </p><div><div><span>$$ u_t(x,t)+6u(x,t)u(-x,-t)u_x(x,t)+u_{xxx}(x,t)=0, $$</span></div></div><p>with the oscillating step-like boundary conditions: <span>(u(x,t)rightarrow 0)</span> as <span>(xrightarrow -infty )</span> and <span>(u(x,t)backsimeq Acos (2Bx+8B^3t))</span> as <span>(xrightarrow infty )</span>, where <span>(A,B&gt;0)</span> are arbitrary constants. The main goal is to develop the Riemann–Hilbert formalism for this problem, paying a particular attention to the case of the “pure oscillating step” initial data, that is, <span>(u(x,0)=0)</span> for <span>(x&lt;0)</span> and <span>(u(x,0)=Acos (2Bx))</span> for <span>(xge 0)</span>. Also, we derive three new families of two-soliton solutions, which correspond to the values of <i>A</i> and <i>B</i> satisfying <span>(B&lt;frac{A}{4})</span>, <span>(B&gt;frac{A}{4})</span> and <span>(B=frac{A}{4})</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02119-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}