On the beta function in supersymmetric gauge theories

Abstract We find the three-loop contribution to the $$\beta $$β-function of $$\mathcal{N}=1$$N=1 supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev–Popov ghosts. This is done using a recently proposed algorithm, which essentially simplifies such multiloop calculations. The result is presented in the form of an integral of double total derivatives in the momentum space. The considered contribution to the $$\beta $$β-function is compared with the two-loop anomalous dimension of the Faddeev–Popov ghosts. This allows verifying the validity of the NSVZ equation written as a relation between the $$\beta $$β-function and the anomalous dimensions of the quantum superfields. It is demonstrated that in the considered approximation the NSVZ equation is satisfied for the renormalization group functions defined in terms of the bare couplings. The necessity of the nonlinear renormalization for the quantum gauge superfield is also confirmed.

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The beta function in supersymmetric gauge theories. Instantons versus traditional approach

Physics Letters B ◽

10.1016/0370-2693(86)90810-5 ◽

1986 ◽

Vol 166 (3) ◽

pp. 329-333 ◽

Cited By ~ 195

Author(s):

V.A. Novikov ◽

M.A. Shifman ◽

A.I. Vainshtein ◽

V.I. Zakharov

Keyword(s):

Gauge Theories ◽

Traditional Approach ◽

Beta Function ◽

Supersymmetric Gauge Theories ◽

Supersymmetric Gauge

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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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