We analyze the large-N expansion of general non-equilibrium systems with fluctuating matrix degrees of freedom and SU (N ) symmetry, using the Schwinger-Keldysh formalism and its closed real-time contour with a forward and backward component. In equilibrium, the large-N expansion of such systems leads to a sum over topologies of two-dimensional surfaces of increasing topological complexity, predicting the possibility of a dual description in terms of string theory. We extend this argument away from equilibrium, and study the universal features of the topological expansion in the dual string theory. We conclude that in non-equilibrium string perturbation theory, the sum over worldsheet topologies is further refined: Each worldsheet surface Σ undergoes a triple decomposition into the part Σ + corresponding to the forward branch of the time contour, the part Σ − on the backward branch, and the part Σ ∧ that corresponds to the instant in the far future where the two branches of the time contour meet. The sum over topologies becomes a sum over the triple decompositions. We generalize our findings to the Kadanoff-Baym time contour relevant for systems at finite temperature, and to the case of closed and open, oriented or unoriented strings. Our results are universal, and follow solely from the features of the large-N expansion without any assumptions about the worldsheet dynamics.

We present a semiclassical proof of the weak gravity conjecture in D = 4 spacetime dimensions for scalar matter gauged under a U (1) N gauge group. We compute the non-perturbative macroscopic entropy of a scalar field in an extremal black hole background at the level of linearized backreaction on the metric. The scalar field is assumed to violate or saturate the weak gravity conjecture. The scalar contributes a logarithmic correction to the entropy in the black hole geometry that outgrows the classical contribution. We demonstrate that the entropy of the gauged scalar violates the generalized second law in the limit of large black hole charge. Our result suggests that entropy inequalities may directly discriminate between effective field theories that live in the landscape versus the swampland.

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We extend our study of the large-N expansion of general non-equilibrium manybody systems with matrix degrees of freedom M , and its dual description as a sum over surface topologies in a dual string theory, to the Keldysh-rotated version of the Schwinger-Keldysh formalism. The Keldysh rotation trades the original fields M ± -defined as the values of M on the forward and backward segments of the closed time contour -for their linear combinations M cl and M qu , known as the "classical" and "quantum" fields. First we develop a novel "signpost" notation for non-equilibrium Feynman diagrams in the Keldysh-rotated form, which simplifies the analysis considerably. Before the Keldysh rotation, each worldsheet surface Σ in the dual string theory expansion was found to exhibit a triple decomposition into the parts Σ ± corresponding to the forward and backward segments of the closed time contour, and Σ ∧ which corresponds to the instant in time where the two segments meet. After the Keldysh rotation, we find that the worldsheet surface Σ of the dual string theory undergoes a very different natural decomposition: Σ consists of a "classical" part Σ cl , and a "quantum embellishment" part Σ qu . We show that both parts of Σ carry their own independent genus expansion. The non-equilibrium sum over worldsheet topologies is naturally refined into a sum over the double decomposition of each Σ into its classical and quantum part. We apply this picture to the classical limits of the quantum non-equilibrium system (with or without interactions with a thermal bath), and find that in these limits, the dual string perturbation theory expansion reduces to its appropriately defined classical limit.