Deformation quantizations from vertex operator algebras

Pan, Yiwen; Peelaers, Wolfger

doi:10.1007/jhep06(2020)127

Cited by 16 publications

(12 citation statements)

References 53 publications

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“…If h 0 a = 0, then [48] Recall that when a is a conformal descendant, o(a [−ha] ) = 0. The first term plays crucial role when dimensionally reducing torus correlators to topological ones on a circle [49,50].…”

Section: Discussionmentioning

confidence: 99%

Defects, modular differential equations, and free field realization of N = 4 VOAs

Pan,

Wang,

Zheng

2021

Preprint

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For all 4d N = 4 SYM theories with simple gauge groups G, we show that the residues of the integrands in the N = 4 Schur indices, which are related to Gukov-Witten type surface defects in the theories, equal the vacuum characters of rank G copies of bcβγ systems that provide the free field realization of associated N = 4 VOAs in [1]. This result predicts that these residues, as module characters, are additional solutions to the flavored modular differential equations satisfied by the original Schur index. The prediction is verified in the G = SU (2) case, where an additional logarithmic solution is constructed.

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Section: Discussionmentioning

confidence: 99%

Defects, modular differential equations, and free field realization of N = 4 VOAs

Pan,

Wang,

Zheng

2021

Preprint

Self Cite

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“…The algebras themselves can be identified either in the SCFT context [4,5], or using the Omega-background [12][13][14] applied to 3d N = 4 theories [24][25][26][27][28] (which uses Omega-deformations of the A and B models [24,29,30]), or from the S 3 supersymmetric background [6][7][8]. For some recent progress on the latter approach see [9,[31][32][33][34][35][36][37][38]. In principle, this list may continue, as any background that is "equivariant" in the appropriate sense can be used for this purpose: for example, the 1d sector construction was recently extended to other backgrounds, such as S 2 × S 1 , see [39].…”

Section: Jhep12(2021)050mentioning

confidence: 99%

Algebras, traces, and boundary correlators in $$ \mathcal{N} $$ = 4 SYM

Dedushenko

Gaiotto

2021

J. High Energ. Phys.

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We study supersymmetric sectors at half-BPS boundaries and interfaces in the 4d $$ \mathcal{N} $$ N = 4 super Yang-Mills with the gauge group G, which are described by associative algebras equipped with twisted traces. Such data are in one-to-one correspondence with an infinite set of defect correlation functions. We identify algebras and traces for known boundary conditions. Ward identities expressing the (twisted) periodicity of the trace highly constrain its structure, in many cases allowing for the complete solution. Our main examples in this paper are: the universal enveloping algebra $$ U\left(\mathfrak{g}\right) $$ U g with the trace describing the Dirichlet boundary conditions; and the finite W-algebra $$ \mathcal{W}\left(\mathfrak{g},{t}_{+}\right) $$ W g t + with the trace describing the Nahm pole boundary conditions.

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“…More recently, a correspondence between a β-γ system on the two-torus and N = 2 theories on S 3 × S 1 was also established [13,14]. The link between three and four dimensions was explored in [15][16][17]. Notably, for four-dimensional theories it has not yet been possible to deviate from the conformal point since the dualities explored in [12][13][14] make explicit use of features exclusive to superconformal field theories, such as non-trivial U(1) r R-symmetry background fields.…”

Section: Jhep09(2020)185mentioning

confidence: 99%

Topological correlators and surface defects from equivariant cohomology

Panerai

Pittelli

Polydorou

2020

J. High Energ. Phys.

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We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

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Deformation quantizations from vertex operator algebras

Cited by 16 publications

References 53 publications

Defects, modular differential equations, and free field realization of N = 4 VOAs

Defects, modular differential equations, and free field realization of N = 4 VOAs

Algebras, traces, and boundary correlators in $$ \mathcal{N} $$ = 4 SYM

Topological correlators and surface defects from equivariant cohomology

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