4d Conformal Field Theories and Strings on Orbifolds

TL;DR

This paper explores the correspondence between 4d conformal field theories with various supersymmetries and Type IIB string theory on orbifolds, proposing mechanisms for stable non-supersymmetric vacua with small cosmological constants.

Contribution

It introduces a new correspondence between 4d conformal theories and string orbifolds, including non-supersymmetric cases with potential for stable vacua.

Findings

Conformal fixed lines exist for these theories.

Potential for non-supersymmetric stable vacua.

Mechanism for small cosmological constant at nontrivial coupling.

Abstract

We propose correspondences between 4d quantum field theories with N=2,1,0 (super)conformal invariance and Type IIB string theory on various orbifolds. We argue using the spacetime string theory, and check using the beta functions (exactly for N=2,1 and so far at 1-loop for the gauge couplings in the N=0 case), that these theories have conformal fixed lines. The latter case potentially gives well-defined non-supersymmetric vacua of string theory, with a mechanism for making the curvature and cosmological constant small at nontrivial string coupling. We suggest a correspondence between nonsupersymmetric conformal fixed lines and nonsupersymmetric string vacua with vanishing vacuum energy.