Mock modular index of M2-M5 brane systems

Abstract

Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review D 96, 026017 c (2017) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We present Bogomolny-Prasad-Sommerfield (BPS) indices of the supergroup Wess-Zumino-Witten (WZW) models that live on intersecting M2-M5-brane systems. They can encode data of the stretched M2-branes between M5-branes and count the BPS states. They are generally expressed in terms of mock theta functions via the Kac-Wakimoto character formula of the affine Lie superalgebra. We give an explicit expression of the index for the PSLð2j2Þ k¼1 WZW model in terms of the second-order multivariable AppellLerch sum. It indicates that wall crossing occurs in the BPS state counting due to the C field on the M5-branes.

Matrix supergroup Chern-Simons models for vortex-antivortex systems

“…In this brane setup the large N limit of the Chern-Simons matrix model corresponds to an infinite number of intersecting M2-branes, which would lead to an M5-brane as a condensate of M2-branes. In [58,59] we found that a certain configuration of intersecting M2-M5 branes on a two-dimensional plane can be effectively described by the supergroup WZW model associated to the affine Lie superalgebra. Since we have found a connection to the affine Lie superalgebra in this work, we believe that further physical explanation and application can be available in string and M-theory.…”

Abelian dualities of $$ \mathcal{N} $$ = (0, 4) boundary conditions

“…• Boundary conditions for N ≥ 4 Chern-Simons matter theories: It would be intriguing to understand N = (0, 4) boundary conditions for 3d N ≥ 4 Chern-Simons matter theories [50,51,52]. The analysis of N = (0, 2) boundary conditions for 3d N = 2 Yang Mills-Chern-Simons theories in [30], which argues the level-rank duality of boundary conditions, may be generalized by including two-dimensional chiral superalgebras [28,53], as the construction of these theories is intimately related to the supergroup structure.…”

Domain walls and M2-branes partition functions: M-theory and ABJM Theory

“…In particular a configuration of an NS5-brane with N D3-branes ending on its left and M D3-branes ending on its right can be associated with the dominant integrable weight λ of u(N|M). The same discussion has been done in the context of a configuration consisting of an M5-brane with an M2brane on only one side [29,30]. In this work some particular indices were calculated for this system and its relation to the highest weight atypical module was elucidated using the Kac-Wakimoto formula.…”

“…We begin this section by reviewing the supergroup WZW models. The supergroup WZW model [29,30] is described by the maps f : Σ → (supergroup)SG from a two dimensional Euclidean Riemann surface Σ to the supergroup SG and its dynamics is given by the action…”