Asymptotic $ \mathcal{W} $ -symmetries in three-dimensional higher-spin gauge theories

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

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BRST and Superfield Formalism—A Review

Universe ◽

10.3390/universe7080280 ◽

2021 ◽

Vol 7 (8) ◽

pp. 280

Author(s):

Loriano Bonora ◽

Rudra Prakash Malik

Keyword(s):

Riemannian Geometry ◽

Gauge Theories ◽

Original Material ◽

Comprehensive Description ◽

Higher Spin ◽

Gauge Anomalies

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories, we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess–Zumino terms for which the formalism seems to be particularly tailor-made. The next subject covered is the higher spin YM-like theories and their anomalies. Finally, we show that the BRST superfield formalism applies as well to the N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.

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Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

International Journal of Modern Physics A ◽

10.1142/s0217751x19300114 ◽

2019 ◽

Vol 34 (23) ◽

pp. 1930011 ◽

Cited By ~ 4

Author(s):

Cyril Closset ◽

Heeyeon Kim

Keyword(s):

Correlation Functions ◽

Gauge Theories ◽

Three Dimensional ◽

Partition Functions ◽

Exact Results ◽

Strongly Coupled ◽

Seifert Manifolds ◽

Recent Developments ◽

Supersymmetric Gauge ◽

Chern Simons

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

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