D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades

TL;DR

This work identifies and clarifies the distinct notions of charges in gravity duals of 2+1D gauge theories, showing how Maxwell, Page, and brane charges behave in ABJM/ABJ-type backgrounds and in ${ m N}=4$ and ${ m N}=3$ theories. It demonstrates that a half-integer shift in torsion flux, arising from Freed-Witten anomalies, is essential for consistent charge quantization and duality framing, and it connects these shifts to brane-creation effects and Seiberg-like transitions. The paper also argues for possible duality cascades in ${ m N}=3$ YM-CS theories, paralleling Klebanov–Strassler cascades, and outlines multiple consistency checks (domain walls, baryon vertices, and parity) that support the revised quantization picture. These results illuminate how IR fixed points and UV couplings are encoded in the global brane and flux data, with implications for holographic descriptions of 2+1D gauge dynamics and their IR/UV dualities.

Abstract

We perform a systematic analysis of the D-brane charges associated with string theory realizations of d=3 gauge theories, focusing on the examples of the N=4 supersymmetric U(N)xU(N+M) Yang-Mills theory and the N=3 supersymmetric U(N)xU(N+M) Yang-Mills-Chern-Simons theory. We use both the brane construction of these theories and their dual string theory backgrounds in the supergravity approximation. In the N=4 case we generalize the previously known gravitational duals to arbitrary values of the gauge couplings, and present a precise mapping between the gravity and field theory parameters. In the N=3 case, which (for some values of N and M) flows to an N=6 supersymmetric Chern-Simons-matter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B-field in the IR solution by 1/2, in units where its periodicity is one, compared to previous claims. We also suggest that the N=3 theories may exhibit, for some values of N and M, duality cascades similar to those of the Klebanov-Strassler theory.

Figures (8)

• Figure 1: The effective gauge couplings of the two gauge groups on the moduli space, as a function of the moduli space coordinate; in theories with eight supercharges this may also be interpreted as the effective running coupling at a particular scale. Figure (a) represents the $k=0$ case where the cascade terminates in the IR with an enhancon. Figure (b) represents a cascade ending when $k > 2 N_4$, so that the effective gauge couplings become small as $\Phi \to 0$ (and there may be a non-trivial SCFT there).
• Figure 2: The solution to the harmonic equation in the decoupling limit, for $k=0$.
• Figure 3: The brane configuration describing a $U(N_2)\times U(N_2+N_4)$ theory with $N_6$ additional flavors charged under $U(N_2)$. The vertical solid lines represent the NS5-branes oriented along the 012345 directions. The horizontal solid lines represent the D3-branes extended along the 0126 directions. The $\times$ represents the D5-brane extended along the 012789 directions. The vertical direction in the figure represents one of the 345 directions, whereas the horizontal direction in the figure represents the $x^6$ coordinate. The vertical dashed lines in the figure are identified as a result of the compactification along the $x^6$ direction. The $N_4$ fractional D3-branes stretch between the NS5-branes, whereas $N_2$ integer D3-branes stretch around the periodic direction. Similar conventions apply to all of our brane diagrams.
• Figure 4: The same brane configuration after moving the NS5-brane on the right around the circle to the right (on the left), and (on the right) the same configuration after also moving the D5-branes to the right.
• Figure 6: The "basic transition" that creates fractional branes when two NS5-branes cross each other in the presence of a D5-brane between them.