[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-272628-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-272628-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","new-rg-flows-between-non-unitary-cfts-from-exact-massless-scattering-theories","New RG flows between non-Unitary CFTs from exact massless scattering theories","","We construct complete solutions to the massless S-matrix bootstrap equations, yielding a new infinite family of integrable renormalization-group flows. The flows connect higher-fusion-level minimal models M(3,2n+3;n) to non-unitary Virasoro minimal models M(2,2n+3), including the case M(3,5) → Yang–Lee CFT M(2,5) at n=1. Identification is supported by matching conformal perturbation theory near UV fixed points to small-volume TBA expansions. We also show that non-invertible Verlinde defect lines are preserved along the flows.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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authors construct in this work?","Question",{"text":63,"@type":64},"They construct complete solutions of the massless S-matrix bootstrap equations for an infinite family of integrable RG flows between specific non-unitary CFTs.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which CFTs are connected by the RG flows?",{"text":68,"@type":64},"The flows go from higher-fusion-level minimal models M(3,2n+3;n) to non-unitary Virasoro minimal models M(2,2n+3), including M(3,5) to the Yang–Lee CFT M(2,5) when n=1.",{"name":70,"@type":61,"acceptedAnswer":71},"How is the proposed identification between flows supported?",{"text":72,"@type":64},"The work matches conformal perturbation theory around the UV fixed points with the small-volume expansion of the corresponding thermodynamic Bethe ansatz equations.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},272628,1789466525,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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massless scattering theories  \nChangrim Ahna 1, Zoltan Bajnokb 2, and Soma Elekb,c 3  \na Department of Physics,  \nEwha Womans University  \nSeoul 120-750, Korea  \nb HUN-REN Wigner Research Centre for Physics,  \nKonkoly-Thege Miklós út 29-33, 1121 Budapest, Hungary  \nc Roland Eötvös University, Department for Theoretical Physics,  \n1117 Budapest, Pázmány sétány 1/A, Hungary  \nPACS: 11.25.Hf, 11.55.Ds  \nAbstract  \nWe construct complete solutions of the massless S-matrix bootstrap equations describing a new infinite family of integrable RG flows from the higher-fusion-level minimal models M(3 , 2n+3;n) to the non-unitary Virasoro minimal models M(2 , 2n+3), including a flow from M(3 , 5) to the Yang–Lee CFT M(2 , 5) when n = 1 . We provide strong evidence for this identification by matching conformal perturbation theory around the UV fixed points with the small-volume expansion of the corresponding thermodynamic Bethe ansatz equations. We further show that a family of non-invertible Verlinde defect lines is preserved along the flows.  \n[1](1 ahn@ewha.ac.kr)[ ahn@ewha.ac.kr](1 ahn@ewha.ac.kr)  \n[2](2 bajnok.zoltan@wigner.hu)[ bajnok.zoltan@wigner.hu](2 bajnok.zoltan@wigner.hu)[ ](2 bajnok.zoltan@wigner.hu)[3](3 elek.soma@wigner.hu)[ elek.soma@wigner.hu](3 elek.soma@wigner.hu)  \n1 Introduction  \nRenormalization-group (RG) flows between conformal field theories (CFTs) provide a fundamental organizing principle in quantum field theory. They describe how the effective degrees of freedom and interactions change with the energy scale, interpolating between ultraviolet (UV) and infrared (IR) fixed points. Distinct UV theories may flow to the same IR CFT, thereby revealing universal long-distance behavior that is insensitive to microscopic details.  \nIn two dimensions, conformal symmetry provides exceptionally powerful tools for characterizing the fixed points through their central charges, operator spectra, and correlation functions. RG flows between unitary two-dimensional CFTs have consequently been studied by a wide range of analytical and numerical methods. A central structural result is Zamolodchikov’s c-theorem, which establishes the existence of a function that decreases monotonically along unitary RG flows and coincides with the central charge at the fixed points [1, 2] . In particular, a unitary flow from a UV CFT to an IR CFT must satisfy cUV > cIR .  \nThe situation is considerably less constrained for non-unitary theories. Reflection positivity is absent, and neither the monotonicity argument underlying the c-theorem nor the usual ordering of fixed points by their central charges applies directly. Nevertheless, nonunitary CFTs and the RG flows connecting them arise naturally in statistical mechanics, critical phenomena, and integrable quantum field theory. Understanding such flows therefore offers a setting in which to investigate universality and exact RG dynamics beyond the unitary paradigm.  \nA standard approach to two-dimensional RG flows is to perturb a conformal field theory by a relevant operator and analyze the resulting theory using conformal perturbation theory or an effective Ginzburg–Landau description. For integrable quantum field theories, the thermodynamic Bethe ansatz (TBA) provides a powerful non-perturbative framework for following the flow between fixed points. Its derivation, however, requires the exact scattering data of the interpolating theory. In many examples these S-matrices are not known, so the proposed TBA equations—and hence the associated RG flows—remain conjectural.  \nA complementary strategy was introduced in [3] . One seeks a massless integrable scattering theory that describes an RG flow generated by a relevant perturbation of a  \nUV CFT and terminating at a prescribed IR CFT. Viewed from the infrared, the same trajectory is obtained by deforming the IR fixed point by irrelevant operators. In the und","cbCaikRBduR4hEX2","https://ap.wps.com/l/cbCaikRBduR4hEX2","pdf",585692,42,"English","# Abstract\n# Introduction\n## Background on RG flows and CFT fixed points\n## Non-unitary theories and the limits of c-theorem methods\n## Perturbative and TBA-based strategies for RG flows\n## Massless integrable scattering and left-right factorization\n## Bootstrap constraints on mixed-chirality amplitudes\n## Analytic structure, poles, and fusion consistency","[{\"question\":\"What do the authors construct in this work?\",\"answer\":\"They construct complete solutions of the massless S-matrix bootstrap equations for an infinite family of integrable RG flows between specific non-unitary CFTs.\"},{\"question\":\"Which CFTs are connected by the RG flows?\",\"answer\":\"The flows go from higher-fusion-level minimal models M(3,2n+3;n) to non-unitary Virasoro minimal models M(2,2n+3), including M(3,5) to the Yang–Lee CFT M(2,5) when n=1.\"},{\"question\":\"How is the proposed identification between flows supported?\",\"answer\":\"The work matches conformal perturbation theory around the UV fixed points with the small-volume expansion of the corresponding thermodynamic Bethe ansatz equations.\"}]","New RG flows between non-Unitary CFTs from exact massless scattering theories | PDF",106]