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Effective potential in non-supersymmetric SU(N) x SU(N) gauge theory and interactions of type 0 D3-branes

A. A. Tseytlin, K. Zarembo

TL;DR

This work analyzes short-distance interactions of parallel D3-branes in type 0 string theory by computing the one-loop effective potential in the non-supersymmetric SU(N) × SU(N) gauge theory that arises as a Z_2 projection of U(2N) N=4 SYM. The bosonic and fermionic contributions combine to yield a potential that vanishes for self-dual configurations, while revealing instability against the separation of multiple like-type branes, though this instability is expected to be suppressed in the large N limit. Finite temperature analysis shows the instability is lifted and a symmetry-restoring transition occurs at $T_c \sim \Lambda$, with branes clustering at high temperature. The results align with a large-$N$ CFT interpretation and imply that the perturbative instability is non-dominant in the planar limit, consistent with an orbifold relation to ${\cal N}=4$ SYM and a potential dual description in type 0 string theory on $AdS_5\times S^5$ with equal fluxes.

Abstract

We study some aspects of short-distance interaction between parallel D3-branes in type 0 string theory as described by the corresponding world-volume gauge theory. We compute the one-loop effective potential in the non-supersymmetric SU(N) x SU(N) gauge theory (which is a Z_2 projection of the U(2N) n=4 SYM theory) representing dyonic branes composed of N electric and N magnetic D3-branes. The branes of the same type repel at short distances, but an electric and a magnetic brane attract, and the forces between self-dual branes cancel. The self-dual configuration (with the positions of the electric and the magnetic branes, i.e. the diagonal entries of the adjoint scalar fields, being the same) is stable against separation of one electric or one magnetic brane, but is unstable against certain modes of separation of several same-type branes. This instability should be suppressed in the large N limit, i.e. should be irrelevant for the large N CFT interpretation of the gauge theory suggested in hep-th/9901101.

Effective potential in non-supersymmetric SU(N) x SU(N) gauge theory and interactions of type 0 D3-branes

TL;DR

This work analyzes short-distance interactions of parallel D3-branes in type 0 string theory by computing the one-loop effective potential in the non-supersymmetric SU(N) × SU(N) gauge theory that arises as a Z_2 projection of U(2N) N=4 SYM. The bosonic and fermionic contributions combine to yield a potential that vanishes for self-dual configurations, while revealing instability against the separation of multiple like-type branes, though this instability is expected to be suppressed in the large N limit. Finite temperature analysis shows the instability is lifted and a symmetry-restoring transition occurs at , with branes clustering at high temperature. The results align with a large- CFT interpretation and imply that the perturbative instability is non-dominant in the planar limit, consistent with an orbifold relation to SYM and a potential dual description in type 0 string theory on with equal fluxes.

Abstract

We study some aspects of short-distance interaction between parallel D3-branes in type 0 string theory as described by the corresponding world-volume gauge theory. We compute the one-loop effective potential in the non-supersymmetric SU(N) x SU(N) gauge theory (which is a Z_2 projection of the U(2N) n=4 SYM theory) representing dyonic branes composed of N electric and N magnetic D3-branes. The branes of the same type repel at short distances, but an electric and a magnetic brane attract, and the forces between self-dual branes cancel. The self-dual configuration (with the positions of the electric and the magnetic branes, i.e. the diagonal entries of the adjoint scalar fields, being the same) is stable against separation of one electric or one magnetic brane, but is unstable against certain modes of separation of several same-type branes. This instability should be suppressed in the large N limit, i.e. should be irrelevant for the large N CFT interpretation of the gauge theory suggested in hep-th/9901101.

Paper Structure

This paper contains 6 sections, 28 equations, 3 figures.

Table of Contents

  1. Introduction
  2. One-loop effective potential
  3. Some properties of effective potential
  4. Effective potential at non-zero temperature
  5. Discussion
  6. Acknowledgements

Figures (3)

  • Figure 1: Interaction potential (\ref{['en']}) between two electric branes.
  • Figure 2: Interaction potential (\ref{['vferm']}) between an electric and a magnetic brane.
  • Figure 3: Interaction potential between electric branes for different temperatures. The potential is normalized so that $V(0,T)=0$.