NON-RENORMALIZABILITY OF THE MASSIVE N = 2 SUPER-YANG–MILLS THEORY

1991 ◽  
Vol 06 (23) ◽  
pp. 2143-2154 ◽  
Author(s):  
G. A. KHELASHVILI ◽  
V. I. OGIEVETSKY
Keyword(s):  
Perturbation Theory ◽  
Fourth Order ◽  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Harmonic Superspace ◽  
Yang Mills ◽  
Super Yang Mills Theory

The massive N = 2 supersymmetric Yang–Mills theory is investigated. Its non-renormalizability is revealed starting from the fourth order of the perturbation theory. The N = 2 harmonic superspace approach and the Stueckelberg-like formalism are used. The Stueckelberg fields form some nonlinear sigma model. Non-renormalizability of the latter produces non-renormalizability of the N = 2 supersymmetric Yang–Mills theory.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

STOCHASTIC QUANTIZATION AND 1/N EXPANSION

1993 ◽  
Vol 08 (02) ◽  
pp. 115-128
Author(s):  
J.C. BRUNELLI ◽  
R.S. MENDES
Keyword(s):  
Perturbation Theory ◽  
Sigma Model ◽  
Functional Approach ◽  
Two Dimensions ◽  
Field Theories ◽  
Nonlinear Sigma Model ◽  
Stochastic Quantization ◽  
Quantization Method ◽  
Systematic Procedure

We study the 1/N expansion of field theories in the stochastic quantization method of Parisi and Wu using the supersymmetric functional approach. This formulation provides a systematic procedure to implement the 1/N expansion which resembles the ones used in the equilibrium. The 1/N perturbation theory for the nonlinear sigma-model in two dimensions is worked out as an example.

Junctions of mass-deformed nonlinear sigma models on SO(2N)/U(N) and Sp(N)/U(N). Part II

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Taegyu Kim ◽  
Sunyoung Shin
Keyword(s):  
Sigma Models ◽  
Complex Projective Space ◽  
Sigma Model ◽  
Grassmann Manifold ◽  
Nonlinear Sigma Model ◽  
Harmonic Superspace ◽  
Projective Superspace ◽  
Superspace Formalism ◽  
Complex Projective ◽  
Nonlinear Sigma Models

Abstract We construct three-pronged junctions of mass-deformed nonlinear sigma models on SO(2N)/U(N) and Sp(N )/U(N ) for generic N. We study the nonlinear sigma models on the Grassmann manifold or on the complex projective space. We discuss the relation between the nonlinear sigma model constructed in the harmonic superspace for- malism and the nonlinear sigma model constructed in the projective superspace formalism by comparing each model with the $$ \mathcal{N} $$ N = 2 nonlinear sigma model constructed in the $$ \mathcal{N} $$ N = 1 superspace formalism.

scholarly journals superparticle and super-Yang–Mills theory in harmonic superspace

2008 ◽  
Vol 802 (1-2) ◽  
pp. 208-246 ◽  
Author(s):  
I.L. Buchbinder ◽  
O. Lechtenfeld ◽  
I.B. Samsonov
Keyword(s):  
Harmonic Superspace ◽  
Yang Mills ◽  
Super Yang Mills Theory

A CONDENSED MATTER ANALOG OF QCD WITH QUARKS

1994 ◽  
Vol 08 (04) ◽  
pp. 417-428
Author(s):  
R. SHANKAR
Keyword(s):  
Relativistic Theory ◽  
Sigma Model ◽  
Condensed Matter ◽  
Quantum Spin ◽  
Spin Chains ◽  
Nonlinear Sigma Model ◽  
Dirac Fermions ◽  
Quantum Spin Chains ◽  
Yang Mills ◽  
Gauge Interaction

It is well known that the d = 1 + 1 nonlinear sigma model is a remarkable analog of pure Yang-Mills theory in d = 3 + 1 and that the former in turn arises in the study of Quantum Spin Chains. It is shown that, upon doping with holes, the chain is described by a fully relativistic theory of Dirac fermions coupled to the sigma model by a gauge interaction. The theory is seen to mimic QCD with quarks in many remarkable ways.

scholarly journals (N, p, q) HARMONIC SUPERSPACE

1995 ◽  
Vol 10 (27) ◽  
pp. 3901-3919 ◽  
Author(s):  
G.G. HARTWELL ◽  
P.S. HOWE
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Harmonic Superspace ◽  
Curved Space ◽  
Yang Mills ◽  
Invariant Integrals ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
Harmonic Superspaces ◽  
Super Yang Mills Theory

A family of harmonic superspaces associated with four-dimensional Minkowski space-time is described. Applications are made to free massless supermultiplets, invariant integrals and super-Yang-Mills theory. Generalization to curved space-times is performed, with emphasis on conformal supergravities.

scholarly journals Maximally supersymmetric RG flows in 4D and integrability

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
João Caetano ◽  
Wolfger Peelaers ◽  
Leonardo Rastelli
Keyword(s):  
Perturbation Theory ◽  
Closed Form ◽  
Spectral Problem ◽  
Spin Chain ◽  
Closed Form Expression ◽  
Form Expression ◽  
Classical Action ◽  
Yang Mills ◽  
Accidental Symmetry ◽  
Super Yang Mills Theory

Abstract We revisit the leading irrelevant deformation of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory that preserves sixteen supercharges. We consider the deformed theory on S3× ℝ. We are able to write a closed form expression of the classical action thanks to a formalism that realizes eight supercharges off shell. We then investigate integrability of the spectral problem, by studying the spin-chain Hamiltonian in planar perturbation theory. While there are some structural indications that a suitably defined deformation might preserve integrability, we are unable to settle this question by our two-loop calculation; indeed up to this order we recover the integrable Hamiltonian of undeformed $$ \mathcal{N} $$ N = 4 SYM due to accidental symmetry enhancement. We also comment on the holographic interpretation of the theory.

scholarly journals Real Valued Functions for the BFKL Eigenvalue

Universe ◽  
2021 ◽  
Vol 7 (11) ◽  
pp. 444
Author(s):  
Mohammad Joubat ◽  
Alex Prygarin
Keyword(s):  
Perturbation Theory ◽  
Bfkl Equation ◽  
Complex Conjugate ◽  
Yang Mills ◽  
General Space ◽  
Function Of Two Variables ◽  
Super Yang Mills Theory

We consider known expressions for the eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in N=4 super Yang-Mills theory as a real valued function of two variables. We define new real valued functions of two complex conjugate variables that have a definite complexity analogous to the weight of the nested harmonic sums. We argue that those functions span a general space of functions for the BFKL eigenvalue at any order of the perturbation theory.

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