We present explicit computations and conjectures for 2 → 2 scattering matrices in large N U(N ) Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the 't Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering. They have unusual structural features: they include a non-analytic piece localized on forward scattering, and obey modified crossing symmetry rules. We conjecture that these unusual features are properties of S-matrices in all Chern-Simons matter theories. The S-matrix in one of the exchange channels in our paper has an anyonic character; the parameter map of the conjectured Bose-Fermi duality may be derived by equating the anyonic phase in the bosonic and fermionic theories.

Abstract:We study the effective dynamics of black hole horizons in Einstein-Maxwell theory in a large number of spacetime dimensions D. We demonstrate that horizon dynamics may be recast as a well posed initial value problem for the motion of a codimension one non gravitational membrane moving in flat space. The dynamical degrees of freedom of this membrane are its shape, charge density and a divergence free velocity field. We determine the equations that govern membrane dynamics at leading order in the large D expansion. Our derivation of the membrane equations assumes that the solution preserves an SO(D − p − 2) isometry with p held fixed as D is taken to infinity. However we are able to cast our final membrane equations into a completely geometric form that makes no reference to this symmetry algebra.

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An all orders formula for the S-matrix for 2 → 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this S-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the S-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic S-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory S-matrix.

It has recently been shown that the dynamics of black holes in large number of dimensions D can be recast as the dynamics of a probe membrane propagating in the background spacetime which solves Einstein equations without matter. The equations of motion of this membrane are simply the statement of conservation of the stress tensor and charge current defined on this membrane. In this paper we obtain the effective equations of motion for stationary membranes in any empty background both in presence and absence of charge. It turns out that the thermodynamic quantities associated with the stationary membranes that satisfy these effective equations also satisfy the first law of black hole thermodynamics. These stationary membrane equations have some interesting solutions such as charged rotating black holes in flat and AdS backgrounds as well as black ring solutions in large D. arXiv:1806.04637v2 [hep-th] 4 Jul 2018 ContentsRecently the authors of [1][2][3][4] made an observation that in the limit where D 1, the degrees of freedom of the black hole spacetime separate into light degrees with length scale r 0 and heavy degrees with length scale r 0 D , where r 0 is a characteristic length scale associated with black hole horizon. They also showed in [5,6] that the quasinormal modes about a static, spherically symmetric black hole in such a large number of dimensions show a similar separation of scales. So it should be possible 1 See [7-11] for related discussion. 2 See [19-21] for more work in this membrane paradigm. 3 See [22-33] for other work that uses large D expansion.