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Gauge Theory and the Excision of Repulson Singularities

Clifford V. Johnson, Amanda W. Peet, Joseph Polchinski

TL;DR

The authors identify repulson-type naked singularities in brane constructions and show that stringy effects reorganize the branes into an enhançon shell, yielding a smooth geometry with an interior where gauge symmetry is enhanced. They connect this geometric resolution to the moduli-space structure of large-N gauge theories with eight supercharges, finding a striking alignment with Seiberg–Witten theory in certain limits and revealing compelling dual pictures (including NS5-brane bending and ALE/K3 duals) even though a precise weakly coupled gravity dual for the gauge theory remains elusive. The work provides a concrete mechanism for singularity excision in string theory, clarifies the role of the enhançon in the gauge-theory context, and offers a framework for exploring nonperturbative moduli-space dynamics in large-N systems. It also outlines several promising directions, such as extending to product gauge groups, adding hypermultiplets, or exploring finite-temperature and rotated/branes configurations to broaden the duality web.

Abstract

We study brane configurations that give rise to large-N gauge theories with eight supersymmetries and no hypermultiplets. These configurations include a variety of wrapped, fractional, and stretched branes or strings. The corresponding spacetime geometries which we study have a distinct kind of singularity known as a repulson. We find that this singularity is removed by a distinctive mechanism, leaving a smooth geometry with a core having an enhanced gauge symmetry. The spacetime geometry can be related to large-N Seiberg-Witten theory.

Gauge Theory and the Excision of Repulson Singularities

TL;DR

The authors identify repulson-type naked singularities in brane constructions and show that stringy effects reorganize the branes into an enhançon shell, yielding a smooth geometry with an interior where gauge symmetry is enhanced. They connect this geometric resolution to the moduli-space structure of large-N gauge theories with eight supercharges, finding a striking alignment with Seiberg–Witten theory in certain limits and revealing compelling dual pictures (including NS5-brane bending and ALE/K3 duals) even though a precise weakly coupled gravity dual for the gauge theory remains elusive. The work provides a concrete mechanism for singularity excision in string theory, clarifies the role of the enhançon in the gauge-theory context, and offers a framework for exploring nonperturbative moduli-space dynamics in large-N systems. It also outlines several promising directions, such as extending to product gauge groups, adding hypermultiplets, or exploring finite-temperature and rotated/branes configurations to broaden the duality web.

Abstract

We study brane configurations that give rise to large-N gauge theories with eight supersymmetries and no hypermultiplets. These configurations include a variety of wrapped, fractional, and stretched branes or strings. The corresponding spacetime geometries which we study have a distinct kind of singularity known as a repulson. We find that this singularity is removed by a distinctive mechanism, leaving a smooth geometry with a core having an enhanced gauge symmetry. The spacetime geometry can be related to large-N Seiberg-Witten theory.

Paper Structure

This paper contains 8 sections, 58 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Repulson Singularity
  3. The Enhançon Geometry
  4. Gauge Theory
  5. The Search for a Duality
  6. The Metric on Moduli Space
  7. A Tale of Two Duals
  8. Conclusions

Figures (2)

  • Figure 1: The phase diagram for large-$N$ and $\lambda_p R^{3-p}\ll{1}$. Note that when $\lambda_p R^{3-p} \gg 1$, the supergravity plus $SU(2)$ gauge description in section 3 should be valid at all radii below $U_2$: the two SYM phases and the mystery phase disappear.
  • Figure 2: $N$ D$(p+1)$-branes ending on NS5-branes: (a) The classical picture (b) The corrected picture, showing the resulting bending of the NS5-branes for large $gN$. The separated brane is the probe which becomes massless at the enhançon locus, an $S^{4-p}$ (a circle in the figure).