Non Supersymmetric Regular Solutions from Wrapped and Fractional Branes

TL;DR

This work extends gravity/gauge duality to non-supersymmetric, yet globally regular backgrounds built from wrapped five-branes and fractional D3-branes on a deformed conifold. By solving the full second-order equations of motion in the MN and KS frameworks, the authors construct non-SUSY generalizations and analyze how SUSY-breaking deformations affect vacuum energies and gaugino condensates. They map gauge-theory operators to supergravity modes, derive both IR and UV asymptotics, and show that condensates and vacuum energy are encoded in subleading UV data while IR regularity fixes UV parameters, highlighting a deep UV/IR interplay. The results indicate that softly broken theories retain several qualitative SUSY features, including multiple vacua distinguished by condensate phases, and open paths to further study such as glueball spectra and stability analyses with potential implications for holographic approaches to QCD-like dynamics.

Abstract

We present two classes of regular supergravity backgrounds dual to supersymmetric and non-supersymmetric gauge theories living on the world-volume of wrapped branes. In particular we consider the Maldacena Nunez and the Klebanov Strassler models, describing N=1 and N=2 theories, and find their non supersymmetric generalization by explicitly solving the second order equation of motion. We also study various aspects of these solutions, including the supersymmetry breaking issue and the vacuum energy.

Figures (3)

• Figure 1: Dependence of the UV parameters from the IR parameter of the condensate $a(u)$, when the other IR parameters vanish. To the left, the dependence of the mass parameters, to the right that of the vev parameters. The dotted line represents the behavior of $M_a$ and $V_a$, the solid line that of $G_{\infty}$ and $V_G$, the dash-dotted $f_{\infty}$,$V_f$ and the dashed line $M_{\tilde{a}}$ and $V_{\tilde{a}}$. The ordinate of $M_a, f_{\infty}, G_{\infty}$ should be red on the left axes, that of $M_{\tilde{a}}$ on the right one. The plots for the vev parameters have been rescaled to fit in the same graphic, the labels of vertical axes should not be taken as absolute values. Note that both parameters $M_{\tilde{a}}$ and $V_{\tilde{a}}$ of the second condensate $\tilde{a}(u)$ do not depend on the first one $a$, as expected since they are independent operators.
• Figure 2: Behavior of $SO(4)$ solutions as $C_a$ changes from 0 (shortest-dashed line) to -2 (longest-dashed line), with the other IR parameters set to zero. For $C_a > 0$ the solution for the field $a(u)$ diverges.
• Figure 3: Behavior of the solutions for $SU(2)_+$ gauge group for different values of $C_l$: $C_l=0$ is the solid line, dash-dotted lines have $C_l$ positive and increasing while dotted ones have $C_l < 0$. Even if not shown in the figure, all solutions with $C_l \neq 0$ diverge as $u$ goes to infinity