The M2/M5 BPS Partition Functions from Supergravity

Abstract

In the framework of the AdS/CFT duality, we calculate the supersymmetric partition function of the superconformal field theories living in the world volume of either $N$ $M2$-branes or $N$ $M5$-branes. We used the dual supergravity partition function in a saddle point approximation over supersymmetric Black Holes. Since our BHs are written in asymptotically global $Ad{S}_{d+1}$ co-ordinates, the dual SCFTs are in $Rx{S}^d$ for $d=2,5$. The resulting partition function shows phase transitions, constraints on the phase space and allowed us to identify unstable BPS Black hole in the $AdS$ phase. These configurations should correspond to unstable configurations in the dual theory. We also report an intriguing relation between the most general Witten Index, computed in the above theories, and our BPS partition functions.

9 pages, 2 columns, 4 figures, revtex, typos corrected, reference added

References in corpus (22)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• An Index for 4 dimensional Super Conformal Theories
• Modeling Multiple M2's
• Bubbling AdS space and 1/2 BPS geometries
• A toy model for the AdS/CFT correspondence
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Supersymmetry of Anti-de Sitter Black Holes
• Selfdual strings and loop space Nahm equations
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons Theories
• Charged Rotating Black Holes in Four-Dimensional Gauged and Ungauged Supergravities
• Rotating Black Holes in Gauged Supergravities; Thermodynamics, Supersymmetric Limits, Topological Solitons and Time Machines
• Giant gravitons in AdS/CFT (I): matrix model and back reaction
• Non-extremal Charged Rotating Black Holes in Seven-Dimensional Gauged Supergravity
• Equal charge black holes and seven dimensional gauged supergravity
• Instabilities of the Small Black Hole: a view from N=4 SYM
• Thermodynamics at the BPS bound for Black Holes in AdS
• Partition Functions for Membrane Theories
• Euclidean analysis of the entropy functional formalism
• Phase transitions and statistical mechanics for BPS Black Holes in AdS/CFT
• On Uniqueness of supersymmetric Black holes in AdS(5)