Brane Dynamics and Gauge Theory

TL;DR

This review presents a comprehensive map from brane dynamics in string/M-theory to the quantum and classical dynamics of supersymmetric gauge theories across dimensions. It develops a unified brane-based framework—via D-branes, NS5-branes, orientifolds, and M5-branes—capturing key phenomena such as Montonen-Olive duality, Seiberg duality, and Seiberg-Witten geometry, and extending these ideas to 3D, 2D, 5D, and 6D theories. By interpreting gauge-theory moduli spaces as brane configurations and employing dualities as core organizing principles, the work elucidates how branes encode Coulomb/Higgs branches, monopole moduli, and BPS spectra, and it offers geometric realizations of intricate IR fixed points and RG flows. The review also highlights open problems and future directions, including a deeper understanding of fivebrane dynamics, orientifold effects, and extending brane constructions to non-supersymmetric settings, with potential implications for QCD-like theories and beyond.

Abstract

We review some aspects of the interplay between the dynamics of branes in string theory and the classical and quantum physics of gauge theories with different numbers of supersymmetries in various dimensions.

Figures (52)

• Figure 1: Low lying states of fundamental strings with both ends on D-branes describe a $U(1)$ gauge field and $9-p$ scalars living on a single D-brane (a), or a $U(N_c)$ gauge field and $9-p$ adjoint scalars on a stack of $N_c$ D-branes (b).
• Figure 2: An orientifold $p$-plane with two adjacent parallel $Dp$-branes and their mirror images. Fundamental strings stretched between a D-brane and its image are projected out for negative orientifold charge. Others come in mirror pairs.
• Figure 3: The $Dp$ - $D(p+4)$ system consisting of a stack of $N_c$$Dp$-branes parallel to $N_f$$D(p+4)$-branes. Locations in the transverse space $(x^{p+5},\cdots, x^9)$ are labeled by $\vec{x}_a$, $\vec{m}_i$, respectively.
• Figure 4: U-duality relates a fundamental string which ends on a $D3$-brane to other supersymmetric configurations, such as a $Dp$-brane which ends on a $D(p+2)$-brane, and a $Dp$-brane which ends on an NS fivebrane.
• Figure 5: A $Dp$-brane intersecting a $D(p+2)$-brane can split into two disconnected parts which separate along the $D(p+2)$-brane.