Annales Henri Poincaré最新文献

{"title":"Stochastic Quantization of Two-Dimensional (P(Phi )) Quantum Field Theory","authors":"Paweł Duch,&nbsp;Wojciech Dybalski,&nbsp;Azam Jahandideh","doi":"10.1007/s00023-024-01447-w","DOIUrl":"10.1007/s00023-024-01447-w","url":null,"abstract":"<div><p>We give a simple and self-contained construction of the <span>(P(Phi ))</span> Euclidean quantum field theory in the plane and verify the Osterwalder–Schrader axioms: translational and rotational invariance, reflection positivity and regularity. In the intermediate steps of the construction, we study measures on spheres. In order to control the infinite volume limit, we use the parabolic stochastic quantization equation and the energy method. To prove the translational and rotational invariance of the limit measure, we take advantage of the fact that the symmetry groups of the plane and the sphere have the same dimension.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 3","pages":"1055 - 1086"},"PeriodicalIF":1.4,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01447-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141257929","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":"Free Energy Fluctuations of the Bipartite Spherical SK Model at Critical Temperature","authors":"Elizabeth W. Collins-Woodfin,&nbsp;Han Gia Le","doi":"10.1007/s00023-024-01448-9","DOIUrl":"10.1007/s00023-024-01448-9","url":null,"abstract":"<div><p>The spherical Sherrington–Kirkpatrick (SSK) model and its bipartite analog both exhibit the phenomenon that their free energy fluctuations are asymptotically Gaussian at high temperature but asymptotically Tracy–Widom at low temperature. This was proved in two papers by Baik and Lee, for all non-critical temperatures. The case of the critical temperature was recently computed for the SSK model in two separate papers, one by Landon and the other by Johnstone, Klochkov, Onatski, Pavlyshyn. In the current paper, we derive the critical temperature result for the bipartite SSK model. In particular, we find that the free energy fluctuations exhibit a transition when the temperature is in a window of size <span>(n^{-1/3}sqrt{log n})</span> around the critical temperature, the same window as for the SSK model. Within this transitional window, the asymptotic fluctuations of the free energy are the sum of independent Gaussian and Tracy–Widom random variables.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 3","pages":"1087 - 1147"},"PeriodicalIF":1.4,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169979","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":"Schrödinger Operators with Multiple Aharonov–Bohm Fluxes","authors":"Michele Correggi,&nbsp;Davide Fermi","doi":"10.1007/s00023-024-01446-x","DOIUrl":"10.1007/s00023-024-01446-x","url":null,"abstract":"<div><p>We study the Schrödinger operator describing a two-dimensional quantum particle moving in the presence of <span>( N geqslant 1)</span> Aharonov–Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 1","pages":"123 - 163"},"PeriodicalIF":1.4,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01446-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146443","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":"An Elliptic Solution of the Classical Yang–Baxter Equation Associated with the Queer Lie Superalgebra","authors":"Maxim Nazarov","doi":"10.1007/s00023-024-01449-8","DOIUrl":"10.1007/s00023-024-01449-8","url":null,"abstract":"<div><p>A solution of the classical Yang–Baxter equation associated with the queer Lie superalgebra is constructed in terms of Hermite theta functions.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 12","pages":"5339 - 5347"},"PeriodicalIF":1.4,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01449-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141109574","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":"Dually Weighted Multi-matrix Models as a Path to Causal Gravity-Matter Systems","authors":"Juan L. A. Abranches,&nbsp;Antonio D. Pereira,&nbsp;Reiko Toriumi","doi":"10.1007/s00023-024-01442-1","DOIUrl":"10.1007/s00023-024-01442-1","url":null,"abstract":"<div><p>We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model corresponds to the CDT-matrix model introduced by Benedetti and Henson (Phys Lett B 678:222, 2009). We present exact as well as approximate results for the Gaussian averages of characters of a Hermitian matrix <i>A</i> and <span>(A^2)</span> for a given representation and establish the present limitations that prevent us to solve the model analytically. This sets the stage for the formulation of more sophisticated matter models coupled to two-dimensional CDT as dually weighted multi-matrix models providing a complementary view to the standard simplicial formulation of CDT-matter models.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 3","pages":"947 - 1008"},"PeriodicalIF":1.4,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01442-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884870","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":"Energy in Fourth-Order Gravity","authors":"R. Avalos,&nbsp;J. H. Lira,&nbsp;N. Marque","doi":"10.1007/s00023-024-01440-3","DOIUrl":"10.1007/s00023-024-01440-3","url":null,"abstract":"<div><p>In this paper we make a detailed analysis of conservation principles in the context of a family of fourth-order gravitational theories generated via a quadratic Lagrangian. In particular, we focus on the associated notion of energy and start a program related to its study. We also exhibit examples of solutions which provide intuitions about this notion of energy which allows us to interpret it, and introduce several study cases where its analysis seems tractable. Finally, positive energy theorems are presented in restricted situations.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 2","pages":"597 - 673"},"PeriodicalIF":1.4,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884875","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":"Flux Quantization on Phase Space","authors":"Hisham Sati,&nbsp;Urs Schreiber","doi":"10.1007/s00023-024-01438-x","DOIUrl":"10.1007/s00023-024-01438-x","url":null,"abstract":"<div><p>While it has become widely appreciated that (higher) gauge theories need, besides their variational phase space data, to be equipped with “flux quantization laws” in generalized differential cohomology, there used to be no general prescription for how to define and construct the resulting flux-quantized phase space stacks. In this short note, we observe that all higher Maxwell-type equations have solution spaces given by flux densities on a Cauchy surface subject to a higher Gauß law and no further constraint: The metric duality-constraint is all absorbed into the evolution equation away from the Cauchy surface. Moreover, we observe that the higher Gauß law characterizes the Cauchy data as flat differential forms valued in a characteristic <span>(L_infty )</span>-algebra. Using the recent construction of the non-abelian Chern–Dold character map, this implies that compatible flux quantization laws on phase space have classifying spaces whose rational Whitehead <span>(L_infty )</span>-algebra is this characteristic one. The flux-quantized higher phase space stack of the theory is then simply the corresponding (generally non-abelian) differential cohomology moduli stack on the Cauchy surface. We show how this systematic prescription reproduces existing proposals for flux-quantized phase spaces of vacuum Maxwell theory and of the chiral boson and its higher siblings, but reveals that there are other choices of (non-abelian) flux quantization laws even in these basic cases, further discussed in a companion article (Sati and Schreiber in Quantum observables on quantized fluxes. arXiv:2312.13037). Moreover, for the case of NS/RR-fields in type II supergravity/string theory, the traditional “Hypothesis K” of flux quantization in topological K-theory is naturally implied, without the need, on phase space, of the notorious further duality constraint. Finally, as a genuinely non-abelian example we consider flux quantization of the C-field in 11d supergravity/M-theory given by unstable differential 4-Cohomotopy (“Hypothesis H”) and emphasize again that, implemented on Cauchy data, this qualifies as the full phase space without the need for a further duality constraint.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 3","pages":"895 - 919"},"PeriodicalIF":1.4,"publicationDate":"2024-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884876","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":"Lightcone Modular Bootstrap and Tauberian Theory: A Cardy-Like Formula for Near-Extremal Black Holes","authors":"Sridip Pal,&nbsp;Jiaxin Qiao","doi":"10.1007/s00023-024-01441-2","DOIUrl":"10.1007/s00023-024-01441-2","url":null,"abstract":"<div><p>We show that for a unitary modular invariant 2D CFT with central charge <span>(c&gt;1)</span> and having a nonzero twist gap in the spectrum of Virasoro primaries, for sufficiently large spin <i>J</i>, there always exist spin-<i>J</i> operators with twist falling in the interval <span>((frac{c-1}{12}-varepsilon ,frac{c-1}{12}+varepsilon ))</span> with <span>(varepsilon =O(J^{-1/2}log J))</span>. We establish that the number of Virasoro primary operators in such a window has a Cardy-like, i.e., <span>(exp left( 2pi sqrt{frac{(c-1)J}{6}}right) )</span> growth. A similar result is proven for a family of holographic CFTs with the twist gap growing linearly in <i>c</i> and a uniform boundedness condition, in the regime <span>(Jgg c^3gg 1)</span>. From the perspective of near-extremal rotating BTZ black holes (without electric charge), our result is valid when the Hawking temperature is much lower than the “gap temperature.”</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 3","pages":"787 - 844"},"PeriodicalIF":1.4,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01441-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884872","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":"The Small-N Series in the Zero-Dimensional O(N) Model: Constructive Expansions and Transseries","authors":"Dario Benedetti,&nbsp;Razvan Gurau,&nbsp;Hannes Keppler,&nbsp;Davide Lettera","doi":"10.1007/s00023-024-01437-y","DOIUrl":"10.1007/s00023-024-01437-y","url":null,"abstract":"<div><p>We consider the zero-dimensional quartic <i>O</i>(<i>N</i>) vector model and present a complete study of the partition function <i>Z</i>(<i>g</i>, <i>N</i>) and its logarithm, the free energy <i>W</i>(<i>g</i>, <i>N</i>), seen as functions of the coupling <i>g</i> on a Riemann surface. We are, in particular, interested in the study of the transseries expansions of these quantities. The point of this paper is to recover such results using constructive field theory techniques with the aim to use them in the future for a rigorous analysis of resurgence in genuine quantum field theoretical models in higher dimensions. Using constructive field theory techniques, we prove that both <i>Z</i>(<i>g</i>, <i>N</i>) and <i>W</i>(<i>g</i>, <i>N</i>) are Borel summable functions along all the rays in the cut complex plane <span>(mathbb {C}_{pi } =mathbb {C}{setminus } mathbb {R}_-)</span>. We recover the transseries expansion of <i>Z</i>(<i>g</i>, <i>N</i>) using the intermediate field representation. We furthermore study the small-<i>N</i> expansions of <i>Z</i>(<i>g</i>, <i>N</i>) and <i>W</i>(<i>g</i>, <i>N</i>). For any <span>(g=|g| e^{imath varphi })</span> on the sector of the Riemann surface with <span>(|varphi |&lt;3pi /2)</span>, the small-<i>N</i> expansion of <i>Z</i>(<i>g</i>, <i>N</i>) has infinite radius of convergence in <i>N</i>, while the expansion of <i>W</i>(<i>g</i>, <i>N</i>) has a finite radius of convergence in <i>N</i> for <i>g</i> in a subdomain of the same sector. The Taylor coefficients of these expansions, <span>(Z_n(g))</span> and <span>(W_n(g))</span>, exhibit analytic properties similar to <i>Z</i>(<i>g</i>, <i>N</i>) and <i>W</i>(<i>g</i>, <i>N</i>) and have transseries expansions. The transseries expansion of <span>(Z_n(g))</span> is readily accessible: much like <i>Z</i>(<i>g</i>, <i>N</i>), for any <i>n</i>, <span>(Z_n(g))</span> has a zero- and a one-instanton contribution. The transseries of <span>(W_n(g))</span> is obtained using Möbius inversion, and summing these transseries yields the transseries expansion of <i>W</i>(<i>g</i>, <i>N</i>). The transseries of <span>(W_n(g))</span> and <i>W</i>(<i>g</i>, <i>N</i>) are markedly different: while <i>W</i>(<i>g</i>, <i>N</i>) displays contributions from arbitrarily many multi-instantons, <span>(W_n(g))</span> exhibits contributions of only up to <i>n</i>-instanton sectors.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 12","pages":"5367 - 5428"},"PeriodicalIF":1.4,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01437-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839576","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":"CLT for (beta )-Ensembles at High Temperature and for Integrable Systems: A Transfer Operator Approach","authors":"G. Mazzuca,&nbsp;R. Memin","doi":"10.1007/s00023-024-01435-0","DOIUrl":"10.1007/s00023-024-01435-0","url":null,"abstract":"<div><p>In this paper, we prove a polynomial central limit theorem for several integrable models and for the <span>(beta )</span>-ensembles at high temperature with polynomial potential. Furthermore, we connect the mean values, the variances and the correlations of the moments of the Lax matrices of these integrable systems with the ones of the <span>(beta )</span>-ensembles. Moreover, we show that the local functions’ space-correlations decay exponentially fast for the considered integrable systems. For these models, we also established a Berry–Esseen-type bound.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 1","pages":"245 - 316"},"PeriodicalIF":1.4,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01435-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800606","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}