β-functions in large-N supersymmetric gauge theories

We review the connection between QCD and supersymmetric theories. We focus on the non-perturbative large- N (planar) correspondence between one-flavor QCD and pure supersymmetric Yang-Mills theory ([Formula: see text]). We explain how non-perturbative quantities in QCD, such as the quark condensate, can be evaluated by using the corresponding non-perturbative results in supersymmetric gauge theories. The review consists of three parts. The first part is devoted to a review of pure [Formula: see text]. In the second part we introduce "orientifold planar equivalence". The third part is devoted to the implications of planar equivalence for QCD.

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AN INTRODUCTION TO SUPERSYMMETRIC GAUGE THEORIES AND MATRIX MODELS

International Journal of Modern Physics A ◽

10.1142/s0217751x04018038 ◽

2004 ◽

Vol 19 (13) ◽

pp. 2015-2078 ◽

Cited By ~ 30

Author(s):

RICCARDO ARGURIO ◽

GABRIELE FERRETTI ◽

RAINER HEISE

Keyword(s):

Matrix Models ◽

Gauge Theories ◽

Supersymmetric Gauge Theories ◽

Large N ◽

Chiral Ring ◽

Supersymmetric Gauge ◽

The One

We give an introduction to the recently-established connection between supersymmetric gauge theories and matrix models. We begin by reviewing previous material that is required in order to follow the latest developments. This includes the superfield formulation of gauge theories, holomorphy, the chiral ring, the Konishi anomaly and the large N limit. We then present both the diagrammatic proof of the connection and the one based on the anomaly. Our discussion is entirely field theoretical and self contained.

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Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

Journal of High Energy Physics ◽

10.1007/jhep03(2021)043 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Tadashi Okazaki ◽

Douglas J. Smith

Keyword(s):

String Theory ◽

Boundary Conditions ◽

Gauge Theories ◽

Holomorphic Curve ◽

Two Dimensional ◽

Supersymmetric Gauge Theories ◽

Special Lagrangian ◽

Supersymmetric Gauge ◽

M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

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Infinite-dimensional fermionic symmetry in supersymmetric gauge theories

Journal of High Energy Physics ◽

10.1007/jhep08(2021)051 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Thomas T. Dumitrescu ◽

Temple He ◽

Prahar Mitra ◽

Andrew Strominger

Keyword(s):

Ward Identity ◽

Gauge Theories ◽

Soft Photon ◽

Supersymmetric Gauge Theories ◽

Null Infinity ◽

Infinite Dimensional ◽

Charged Matter ◽

Gauge Symmetries ◽

Supersymmetric Gauge

Abstract We establish the existence of an infinite-dimensional fermionic symmetry in four-dimensional supersymmetric gauge theories by analyzing semiclassical photino dynamics in abelian $$ \mathcal{N} $$ N = 1 theories with charged matter. The symmetry is parametrized by a spinor-valued function on an asymptotic S2 at null infinity. It is not manifest at the level of the Lagrangian, but acts non-trivially on physical states, and its Ward identity is the soft photino theorem. The infinite-dimensional fermionic symmetry resides in the same $$ \mathcal{N} $$ N = 1 supermultiplet as the physically non-trivial large gauge symmetries associated with the soft photon theorem.

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