Title: Removal of the trace mode in lattice $\mathcal{N}=4$ super Yang-Mills theory

Abstract

Twisted and orbifold formulations of lattice N = 4 super Yang-Mills theory which possess an exact supersymmetry require a U(N)=SU(N) Ⓧ U(1) gauge group. In the naive continuum limit, the U(1) modes trivially decouple and play no role in the theory. However, at nonzero lattice spacing they couple to the SU(N) modes and can drive instabilities in the lattice theory. For example, it is well known that the lattice U(1) theory undergoes a phase transition at strong coupling to a chirally broken phase. An improved action that suppresses the fluctuations in the U(1) sector was proposed in Catterall and Schaich [J. High Energy Phys. 07 (2015) 057]. Here, we explore a more aggressive approach to the problem by adding a term to the action which can entirely suppress the U(1) mode. The penalty is that the new term breaks the Q-exact lattice supersymmetry. However, we argue that the term is 1/N² suppressed and the existence of a supersymmetric fixed point in the planar limit ensures that any supersymmetry-violating terms induced in the action possess couplings that also vanish in this limit. We present numerical results on supersymmetric Ward identities consistent with this conclusion.

Authors:

Catterall, Simon; Jha, Raghav G.; Giedt, Joel

Publication Date:

Mon Nov 26 00:00:00 EST 2018

Research Org.:

Syracuse Univ., NY (United States); Rensselaer Polytechnic Inst., Troy, NY (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1483343

Alternate Identifier(s):

OSTI ID: 1611301

Grant/Contract Number:  

SC0009998; SC0013496

Resource Type:

Published Article

Journal Name:

Physical Review. D.

Additional Journal Information:

Journal Name: Physical Review. D. Journal Volume: 98 Journal Issue: 9; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics; Supersymmetric models