Superconformal index, BPS monodromy and chiral algebras

Cecotti, Sergio; Song, Jaewon; Vafa, Cumrun; Yan, Wenbin

doi:10.1007/jhep11(2017)013

Cited by 73 publications

(106 citation statements)

References 103 publications

(369 reference statements)

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“…We find this expression agrees with the index in the Macdonald and Schur limits [55,57] computed in [49][50][51][52][53]. Especially, we find that in the Schur limit t → q, the expression becomes independent of p. This is consistent with the expectation that our theory preserves N = 2 supersymmetry in the IR.…”

Section: Jhep02(2017)075supporting

confidence: 89%

“…We have checked that when N = 1, 2, the leading terms for the Macdonald limit p → 0 and Schur limit p → 0, t → q of this integral agrees with the results in [50,52,53] computed using different methods. Especially, in the Hall-Littlewood limit, the index becomes trivial since there is no Higgs branch in this theory.…”

Section: Jhep02(2017)075supporting

confidence: 71%

“…Recently, the superconformal index in various limits for the Argyres-Douglas theory has been computed [49][50][51][52][53][54]. Here, we compute the full superconformal index of the ArgyresDouglas theory using the gauge theory description we obtained.…”

Section: The Full Superconformal Index Of (A 1 a N ) Argyres-douglamentioning

confidence: 99%

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N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs

Maruyoshi

Song

2017

J. High Energ. Phys.

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115

135

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Abstract:We study certain N = 1 preserving deformations of four-dimensional N = 2 superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an N = 1 chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced N = 2 supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the (A 1 , A n ) Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the (A 1 , A n ) theories and find agreements with the previous results. Furthermore, we study the cases, including the T N and R 0,N theories of class S and some of rank-one SCFTs, where the deformation gives genuine N = 1 fixed points.

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Section: Jhep02(2017)075supporting

confidence: 89%

Section: Jhep02(2017)075supporting

confidence: 71%

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N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs

Maruyoshi

Song

2017

J. High Energ. Phys.

Self Cite

115

135

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“…On the other hand, our papers are largely complementary. Indeed, [18] motivates additional conjectures regarding N = 2-perserving chiral ring relations (their equation (11)) that are compatible with our results, while our paper discusses aspects of non-chiral operators, the superconformal index, accidental symmetries, and absence of free fields.…”

Section: Introductionsupporting

confidence: 71%

“…On the other hand, there is evidence that AD theories are particularly simple: their conformal anomalies scale linearly with the dimensions of their Coulomb branches [4,5], and their superconformal indices take a particularly simple form [6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Small deformation of a simple N=2 superconformal theory

Buican

Nishinaka

2016

Phys. Rev. D

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We study an interesting relevant deformation of the simplest interacting N = 2 SCFT-the original Argyres-Douglas (AD) theory. We argue that, although this deformation is not strictly speaking Banks-Zaks like (certain operator dimensions change macroscopically), there are senses in which it constitutes a mild deformation of the parent AD theory: the exact change in the a anomaly is small and is essentially saturated at one loop. Moreover, contributions from IR operators that have a simple description in the UV theory reproduce a particular limit of the IR index to a remarkably high order. These results lead us to conclude that the IR theory is an interacting N = 1 SCFT with particularly small a and c central charges and that this theory sheds some interesting light on the spectrum of its AD parent. Our results also lead us to the conclusion that the theory spaces emanating from some of the simplest N = 1 gauge theories may be richer than anticipated.

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TBA equations and resurgent Quantum Mechanics

Ito

Mariño

Shu

2019

J. High Energ. Phys.

124

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We derive a system of TBA equations governing the exact WKB periods in onedimensional Quantum Mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE/IM correspondence, and they can be regarded as the solution of a Riemann-Hilbert problem in resurgent Quantum Mechanics formulated by Voros. Our derivation builds upon the solution of similar Riemann-Hilbert problems in the study of BPS spectra in N = 2 gauge theories and of minimal surfaces in AdS. We also show that our TBA equations, combined with exact quantization conditions, provide a powerful method to solve spectral problems in Quantum Mechanics. We illustrate our general analysis with a detailed study of PT-symmetric cubic oscillators and quartic oscillators. arXiv:1811.04812v3 [hep-th] 31 Jan 2019Contents -1 -periods involved in the problem. However, this flourishing of ideas did not provide alternative computational methods in Quantum Mechanics. One was supposed to calculate the WKB series and their Borel resummations with traditional tools.Partially inspired by the results of [3], a correspondence between certain quantum mechanical models in one dimension and integrable models (or ODE/IM correspondence) was proposed by Dorey and Tateo in [7]. This correspondence was originally based on functional relations discovered in the context of resurgent Quantum Mechanics, which are similar to Baxter-type equations appearing in integrable systems. The ODE/IM correspondence makes it possible to write down TBA equations which calculate efficiently and exactly some of the quantities appearing in the quantum mechanical models, like spectral determinants and Borel resummations of WKB periods. An important limitation of the ODE/IM correspondence is that it applies to very special quantum-mechanical models, namely, monic potentials of the form V (x) = x M (and a limited amount of perturbations thereof).In this paper we will present TBA equations governing the WKB periods for general polynomial potentials in one dimension, providing in this way a generalization of the ODE/IM correspondence. The basic idea was already pointed out by Voros in his seminal paper [3], where he called it the "analytic bootstrap" for the exact WKB method. In this approach, the fundamental objects are the WKB periods, which are (Borel resummed) perturbative series in the Planck constant. These periods can be characterized by two types of data: their classical limit and their discontinuity structure, which has been known since the work of [3,4,6]. In the theory of resurgence, this discontinuity structure is encoded in the action of the so-called Stokes automorphisms. As Voros explained, we can think about these data as defining a Riemann-Hilbert problem. Building on recent developments in seemingly very different contexts [8][9][10][11][12][13][14][15], we show that Voros' Riemann-Hilbert problem has a solution in terms of a TBA-like system, which determines the exact dependence of the WKB periods on the Planck constant 1 . The TBA system of [7] is recove...

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Superconformal index, BPS monodromy and chiral algebras

Cited by 73 publications

References 103 publications

N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs

N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs

Small deformation of a simple N=2 superconformal theory

TBA equations and resurgent Quantum Mechanics

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