Supergravity and Large N Noncommutative Field Theories

TL;DR

This work extends the AdS/CFT paradigm to noncommutative field theories arising from Dp branes in a constant B field and its M5/NS5 analogs. By deriving the decoupling limits and dual supergravity backgrounds, it identifies phase structures governed by the effective coupling g_eff and the effective noncommutativity a_eff, and shows that gravity can decouple for p >= 6 in these setups. It also computes Wilson loop and Wilson surface observables using moving coordinate frames to handle noncommutative effects, finding results that map to the commutative case with appropriate replacements of the gauge coupling by the noncommutative parameters. The findings illuminate UV/IR connections in large-N noncommutative theories and suggest new gravity-free descriptions in certain brane configurations, with broader implications for M(atrix) theory and six-dimensional (0,2) dynamics.

Abstract

We consider systems of Dp branes in the presence of a nonzero B field. We study the corresponding supergravity solutions in the limit where the branes worldvolume theories decouple from gravity. These provide dual descriptions of large N noncommutative field theories. We analyse the phase structure of the theories and the validity of the different description. We provide evidence that in the presence of a nonzero B field the worldvolume theory of D6 branes decouples from gravity. We analyse the systems of M5 branes and NS5 branes in the presence of a nonzero C field and nonzero RR fields, respectively. Finally, we study the Wilson loops (surfaces) using the dual descriptions.

Figures (10)

• Figure 1: The different descriptions of the D2 branes theory with non-zero $B$ field as a function of the energy scale $u$. We see the flow from ${\cal N}=8$ NCSYM at high energy to ${\cal N}=8$ SCFT at low energy. The plot is for the case $\beta \ll1$ and therefor when we up-lift to eleven dimensions the noncommutativity effects are negligible. When $\beta \gg 1$ the plot is similar, however the transition to eleven dimensions occurs at $u \sim {\bar{g}}_{YM}^{14/15}N^{1/5}b^{1/5}$ and then the noncommutative effects are not negligible.
• Figure 2: The different descriptions of the D4 branes theory with $B$ field ($m=1$) as a function of the energy scale $u$ for $\beta \ll 1$.
• Figure 3: The different descriptions of the D4 branes theory with $B$ field ($m=1$) as a function of the energy scale $u$ for $\beta \gg 1$.
• Figure 4: The transition between the different descriptions of the D5 brane theory with $B$ field ($m=1$) as a function of the energy scale $u$ when $\beta \ll 1$.
• Figure 5: The transition between the different descriptions of the D5 brane theory with $B$ field ($m=1$) as a function of the energy scale $u$ when $\beta \gg 1$.