On the Gauge/Gravity Correspondence and the Open/Closed String Duality

TL;DR

This paper demonstrates that the gauge/gravity correspondence extends beyond supersymmetric theories, asserting its validity when threshold corrections vanish and open/closed string channels exactly map massless contributions. It shows, in detail, how fractional branes on orbifolds and dyonic configurations in Type 0B/0' models reproduce perturbative gauge-theory data from supergravity or string computations, and how planar equivalence underpins these results. The work connects open/closed duality with the background-field method to explain holographic identifications of $1/g_{YM}^2$ and $\theta_{YM}$, and it highlights the role of the enhançon and tachyon-free constructions in sustaining a consistent gauge/gravity picture across both SUSY and non-SUSY settings. Collectively, the findings indicate that holographic insights can apply to a broad class of non-conformal gauge theories, especially in the large-$N$ limit, where planar diagrams dominate.

Abstract

In this article we review the conditions for the validity of the gauge/gravity correspondence in both supersymmetric and non-supersymmetric string models. We start by reminding what happens in type IIB theory on the orbifolds C^2/Z_2 and C^3/(Z_2 x Z_2), where this correspondence beautifully works. In these cases, by performing a complete stringy calculation of the interaction among D3 branes, it has been shown that the fact that this correspondence works is a consequence of the open/closed duality and of the absence of threshold corrections. Then we review the construction of type 0 theories with their orbifolds and orientifolds having spectra free from both open and closed string tachyons and for such models we study the validity of the gauge/gravity correspondence, concluding that this is not a peculiarity of supersymmetric theories, but it may work also for non-supersymmetric models. Also in these cases, when it works, it is again a consequence of the open/closed string duality and of vanishing threshold corrections.

Figures (2)

• Figure 1: One-loop correction to the two-point function with two external background field strengths. These are the diagrams one has to consider when evaluating the one loop running coupling constant of the gauge theory via the background field method. Dashed lines denote the ghost fields.
• Figure 2: Second order expansion in the background field of the one-loop vacuum amplitude of an open string stretching between a stack of $N$ D3 branes and a further brane dressed with an $SU(N)$ background field. The number $N$ of D3 branes encodes the information about the non-abelian nature of the quantum gauge fields propagating in the loop. In the field theory limit this diagram reduces to those in Fig. 1