More on Supersymmetric Domain Walls, N Counting and Glued Potentials

TL;DR

This paper explores the properties of supersymmetric domain walls, including their interpretation, existence conditions, and implications for gauge theories, revealing new insights into their structure and the limitations of current models.

Contribution

It provides a novel field-theoretic interpretation of strings ending on walls and analyzes the existence of BPS walls in theories with glued superpotentials, clarifying the physical origin of the cusp structure.

Findings

Strings can end on domain walls in supersymmetric theories.

The cusp structure limits the calculability of wall tension.

Discrete anomaly matching does not exclude a chirally symmetric phase.

Abstract

Various features of domain walls in supersymmetric gluodynamics are discussed. We give a simple field-theoretic interpretation of the phenomenon of strings ending on the walls recently conjectured by Witten. An explanation of this phenomenon in the framework of gauge field theory is outlined. The phenomenon is argued to be particularly natural in supersymmetric theories which support degenerate vacuum states with distinct physical properties. The issue of existence (or non-existence) of the BPS saturated walls in the theories with glued (super)potentials is addressed. The amended Veneziano-Yankielowicz effective Lagrangian belongs to this class. The physical origin of the cusp structure of the effective Lagrangian is revealed, and the limitation it imposes on the calculability of the wall tension is explained. Related problems are considered. In particular, it is shown that the so called discrete anomaly matching, when properly implemented, does not rule out the chirally symmetric phase of supersymmetric gluodynamics, contrary to recent claims.