Exploring Reggeon bound states in strongly-coupled $$ \mathcal{N} $$ = 4 super Yang-Mills

The multi-Regge limit of scattering amplitudes in strongly-coupled $$ \mathcal{N} $$ N = 4 super Yang-Mills is described by the large mass limit of a set of thermodynamic Bethe ansatz (TBA) equations. A non-trivial remainder function arises in this setup in certain kinematical regions due to excitations of the TBA equations which appear during the analytic continuation into these kinematical regions. So far, these analytic continuations were carried out on a case-by-case basis for the six- and seven-gluon remainder function. In this note, we show that the set of possible excitations appearing in any analytic continuation in the multi-Regge limit for any number of particles is rather constrained. In particular, we show that the BFKL eigenvalue of any possible Reggeon bound state is a multiple of the two-Reggeon BFKL eigenvalue appearing in the six-gluon case.

The inflationary wavefunction from analyticity and factorization

We study the analytic properties of tree-level wavefunction coefficients in quasi-de Sitter space. We focus on theories which spontaneously break dS boost symmetries and can produce significant non-Gaussianities. The corresponding inflationary correlators are (approximately) scale invariant, but are not invariant under the full conformal group. We derive cutting rules and dispersion formulas for the late-time wavefunction coefficients by using factorization and analyticity properties of the dS bulk-to-bulk propagator. This gives a unitarity method which is valid at tree-level for general n-point functions and for fields of arbitrary mass. Using the cutting rules and dispersion formulas, we are able to compute n-point functions by gluing together lower-point functions. As an application, we study general four-point, scalar exchange diagrams in the EFT of inflation. We show that exchange diagrams constructed from boost-breaking interactions can be written as a finite sum over residues. Finally, we explain how the dS identities used in this work are related by analytic continuation to analogous identities in Anti-de Sitter space.

Entanglement between two gravitating universes

We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the n th Rényi entropy includes a wormhole between the n copies of the gravitating universe, leading to a standard “island formula” for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with 2n boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by Ζ n replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a “swap wormhole”, a geometry in which the boundaries of the two universes are glued together by a “swaperator”. This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes – a realization of the ER=EPR idea. The new wormhole restores unitarity of quantum information.

Continuous cosmic evolution with diffusive barotropic fluid: First-order thermodynamic phase transition

In the background of homogeneous and isotropic flat FLRW model, a complete cosmic scenario from nonsingular emergent scenario to the present late time acceleration through inflationary era and matter-dominated epoch has been presented in this work with cosmic matter in the form of diffusive barotropic fluid. By proper choices of the diffusion parameter and using Friedmann equations, it is possible to show the transitions: Emergent scenario[Formula: see text]Inflationary era[Formula: see text]matter-dominated phase[Formula: see text]Late time acceleration epoch. In analogy with analytic continuation, it is found that the above evolution will be continuous for suitable values of the parameters involved. Finally, possible first-order thermodynamic phase transition has been analyzed for such cosmic evolution.

The mean value of the generalized Dirichlet L-functions with the weight of the Gauss sums

Let [Formula: see text] be an integer, and let [Formula: see text] denote a Dirichlet character modulo [Formula: see text]. For any real number [Formula: see text], we define the generalized Dirichlet [Formula: see text]-function as [Formula: see text] where [Formula: see text] with [Formula: see text] and [Formula: see text] both real. It can be extended to all [Formula: see text] using analytic continuation. For any integer [Formula: see text], the famous Gauss sum [Formula: see text] is defined as [Formula: see text] where [Formula: see text]. This paper uses analytic methods to study the mean value properties of the generalized Dirichlet [Formula: see text]-functions with the weight of the Gauss sums, and a sharp asymptotic formula is obtained.