Abstract
We analyze the low temperature structure of a supersymmetric quiver quantum mechanics with randomized superpotential coefficients, treating them as quenched disorder. These theories describe features of the low energy dynamics of wrapped branes, which in large number backreact into extremal black holes. We show that the low temperature theory, in the limit of a large number of bifundamentals, exhibits a time reparametrization symmetry as well as a specific heat linear in the temperature. Both these features resemble the behavior of black hole horizons in the zero temperature limit. We demonstrate similarities between the low temperature physics of the random quiver model and a theory of large $N$ free fermions with random masses.
Highlights
Parameters of this Hamiltonian will result from difficult calculations involving the detailed structure of the compactification manifold
We show that the low temperature theory, in the limit of a large number of bifundamentals, exhibits a time reparametrization symmetry as well as a specific heat linear in the temperature
We demonstrate similarities between the low temperature physics of the random quiver model and a theory of large N free fermions with random masses
Summary
The quantum mechanical theories of interest in this paper have four supercharges [3]. N indicates a particular intersection mode connecting two branes, and the index i = 1, 2, 3, . As mentioned in the introduction, these theories can be viewed as low energy effective actions arising from the dynamics of open strings living at the intersection points of branes wrapped along internal cycles in the compactification manifold. The branes are point like in the non-compact dimensions, and we are discarding their position degrees of freedom (which comprise a vector multiplet) by making them parametrically massive. The details of the coefficients Ωα are contained in the geometry of the compactification manifold and the specific cycles wrapped by the branes. By evaluating a Witten index, the particular model under consideration was shown to have an exact ground state degeneracy that grows as 23N in the large N limit [4]. Our main interest in what follows regards the low temperature nonsupersymmetric sector of the model which has been far less explored
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