Glueballs of Super Yang-Mills from Wrapped Branes

TL;DR

The paper investigates glueball-like excitations in ${ m N}=1$ SYM using holographic models based on wrapped D-branes in type IIB and IIA backgrounds. By analyzing linearized fluctuations, it shows that the scalar $0^{++}$ mode is a mixture of the dilaton and internal metric components and derives a Schrödinger-like equation for the IIB case, which yields a discrete spectrum with a mass gap but non-normalizable states due to UV completion by a little string theory. A regularization procedure is proposed that subtracts the UV abelian background to obtain normalizable states and a numerically stable eigenvalue, highlighting a discrete spectrum even without an explicit IR cut-off. In the IIA perspective, a parallel fluctuation analysis is outlined, with the observation that the dilaton divergence does not occur, potentially avoiding regularization there. The work clarifies the role of KK contamination, provides a framework for extracting qualitative glueball information in wrapped-brane models, and suggests multiple avenues for refining the comparison with lattice results and exploring decoupling of KK modes.

Abstract

In this paper we study qualitative features of glueballs in N=1 SYM for models of wrapped branes in IIA and IIB backgrounds. The scalar mode, 0++ is found to be a mixture of the dilaton and the internal part of the metric. We carry out the numerical study of the IIB background. The potential found exhibits a mass gap and produces a discrete spectrum without any cut-off. We propose a regularization procedure needed to make these states normalizable.

Figures (2)

• Figure 1: VS(r) for different values of $K^2$.
• Figure 2: VS(r) for abelian and non-abelian theories, dashed line and solid lines.