Entanglement Hamiltonians for Chiral Fermions with Zero Modes.

In this Letter, we study the effect of topological zero modes on entanglement Hamiltonians and the entropy of free chiral fermions in (1+1)D. We show how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain exact expressions for entanglement Hamiltonians. In the absence of the zero mode, the resulting entanglement Hamiltonians consist of local and bilocal terms. In the periodic sector, the presence of a zero mode leads to an additional nonlocal contribution to the entanglement Hamiltonian. We derive an exact expression for this term and for the resulting change in the entanglement entropy.

Three-point functions of aging dynamics and the AdS-CFT correspondence.

Aging can be realized as a subalgebra of Schrödinger algebra by discarding the time-translation generator. While the two-point functions of the age algebra have been known for some time, little else was known about the higher n-point correlators. In this Letter, we present novel three-point correlators of scalar primary operators. We find that the aging correlators are distinct from the Schrödinger correlators by more than certain dressings with time-dependent factors, as was the case with two-point functions. In the existing literature, the holographic geometry of aging is obtained by performing certain general coordinate transformations on the holographic dual of the Schrödinger theory. Consequently, the aging two-point functions derived from holography look as the Schrödinger two-point functions dressed by time-dependent factors. However, since the three-point functions obtained in this Letter are not merely dressed Schrödinger correlators and instead, depend on an additional time-translation breaking variable, we conclude that the most general holographic realization of aging is yet to be found. We also comment on various extensions of the Schrödinger and aging algebras.

M theory solution to the hierarchy problem.

An old idea for explaining the hierarchy is strong gauge dynamics. We show that such dynamics also stabilizes the moduli in M theory compactifications on manifolds of G2 holonomy without fluxes. This gives stable vacua with softly broken supersymmetry, grand unification, and a distinctive spectrum of TeV and sub-TeV sparticle masses.

Hadronic density of states from string theory.

We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nùñez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.