N=2 Gauge Theories and Systems with Fractional Branes

TL;DR

This work analyzes the Seiberg-Witten curve for ${ m N}=2$ gauge theories engineered with fractional D3-branes, focusing on the enhançon mechanism that resolves IR singularities in the gravity duals. By lifting to M-theory, it derives an elliptic, $n$-sheeted SW curve whose moduli are tied to fractional versus physical brane data via polynomials $R(v)$ and $S(v)$, and explores the weak-coupling limit to connect to a conformal $SU(n) imes SU(n)$ theory with two bifundamentals. The geometrical enhançon is interpreted as branes dissolving on a circle at scale $ig|vig|= obreak obreak obreak \,\Lambda$, with instanton corrections playing a crucial role in the full quantum structure. Comparison with the Type IIB supergravity solutions shows qualitative agreement in the running couplings and IR resolution, while emphasizing regimes where D1-instantons and tensionless-string phases become important, signaling the limits of a purely supergravity description. Overall, the paper clarifies how Seiberg-Witten data and stringy enhançon physics coherently describe non-conformal ${ m N}=2$ dualities in orbifold backgrounds and informs the AdS/CFT dictionary in these settings.

Abstract

We analyse the Seiberg Witten curve describing the N=2 gauge theory dual to the supergravity solution with fractional branes. Emphasis is given to those aspects that are related to stringy mechanism known as the enhancon. We also compare our results with the features of the supergravity duals, which have been variously interpreted in the literature. Known aspects of the N=2 gauge theories seem to agree with the supergravity solution, whenever the two theories can be faithfully compared.

Figures (4)

• Figure 1: Type IIB and IIA picture for physical and fractional branes.
• Figure 2: The fundamental domain for the torus $E$ and its projection to a circle in type IIA with wrapped D4-branes. The four distinguished points $x=0,1,\lambda,\infty$ in the cubic representation are explicitly indicated.
• Figure 3: The SW curve as $n$-sheeted covering of the torus $E$.
• Figure 4: Positions of the two NS branes on the torus as functions of $v$. The argument of the complex number $v$ has been fixed.