Membranes with topological charge andAdS4/CFT3correspondence

Abstract

If the second Betti number b 2 of a Sasaki-Einstein manifold Y 7 does not vanish, then M-theory on AdS 4 × Y 7 possesses "topological" U (1) b 2 gauge symmetry. The corresponding Abelian gauge fields come from three-form fluctuations with one index in AdS 4 and the other two in Y 7 . We find black membrane solutions carrying one of these U (1) charges. In the zero temperature limit, our solutions interpolate between AdS 4 × Y 7 in the UV andbackground is by itself a solution of the supergravity equations of motion. These solutions do not appear to preserve any supersymmetry. We search for their possible instabilities and do not find any. We also discuss the meaning of our charged membrane backgrounds in a dual quiver ChernSimons gauge theory with a global U (1) charge density. Finally, we present a simple analytic solution which has the same IR but different UV behavior. We reduce this solution to type IIA string theory, and perform T-duality to type IIB. The type IIB metric turns out to be a product of the squashed Y 7 and the extremal BTZ black hole. We discuss an interpretation of this type IIB background in terms of the (1 + 1)-dimensional CFT on D3-branes partially wrapped over the squashed Y

Charged particle-like branes in ABJM

“…As discussed in [10] and further elaborated in a similar context in [11][12][13][14], the two fall-offs are possible in AdS 4 . 2 Choosing one or the other amounts to the dual U(1) symmetry being gauged or not.…”

“…1 More generally, these wrapped branes act as sources to vector fields in AdS 4 arising from the reduction of RR potentials on topologically non-trivial cycles. In turn, vector fields in AdS 4 admit quantization with either of the two possible fall-offs at the boundary [10], which amount to either a dynamical boundary gauge field or to a global current (discussions in this context have appeared recently in [11][12][13][14]). Since a definite quantization must be chosen, it follows that either magnetic or electric sources are forbidden for the corresponding bulk field [10].…”

Weak gravity conjecture in the AdS/CFT correspondence

“…IV C. Recall that this bound is related, in the limit r þ =L → ∞, to the (in)stability of planer extremal AdS-RN black branes, since in this limit the horizon can be approximated by a plane with R 3 topology. In fact, there had been some interests in the stability of these objects in string compactification [12,14,19]. The motivation there was mainly applications to condensed matter physics, in which the instability of these objects corresponds to the instability of zero temperature CFTs under the introduction of chemical potentials.…”

On thermodynamics of charged AdS black holes in extended phases space via M2-branes background

“…All these recent inspiring works on asymptotically AdS 4 black holes in M-theory [28][29][30][31][32] motivate us to study the thermodynamics and thermodynamical geometry of Ad S 4 × S 7 , from the physics of M2-branes, where we interpret the number of M2-branes as a thermodynamical variable as in [1]. We then discuss the stability of such solutions and examine the corresponding first phase transition by analyzing various relevant quantities including the chemical potential, free energy, and heat capacities.…”