On The Entanglement Entropy For Gauge Theories

We propose a definition for the entanglement entropy of a gauge theory on a spatial lattice. Our definition applies to any subset of links in the lattice, and is valid for both Abelian and Non-Abelian gauge theories. For $\mathbb{Z}_N$ and $U(1)$ theories, without matter, our definition agrees with a particular case of the definition given by Casini, Huerta and Rosabal. We also argue that in general, both for Abelian and Non-Abelian theories, our definition agrees with the entanglement entropy calculated using a definition of the replica trick. Our definition, however, does not agree with some standard ways to measure entanglement, like the number of Bell pairs which can be produced by entanglement distillation.

Comments: 29 pages, 4 figures; section on Extended Lattice Construction revised and some changes in referencing; some of the discussion of the replica trick changed; section on SU(2) revised for clarity

Similar Publications

We give a brief overview of the current status of Double Field Theory on Group Manifolds (DFTWZW). Therefore, we start by reviewing some basic notions known from Double Field Theory (DFT) and show how they extend/generalize into the framework of Double Field Theory on Group Manifolds. In this context, we discuss the relationship between both theories and the transition from DFTWZW to DFT. Read More

We study the supersymmetric extensions of the $O(3)$ $\sigma$-model in $1+1$ and $2+1$ dimensions. We show that it is possible to construct non-equivalent supersymmetric versions of a given model sharing the same bosonic sector and free from higher-derivative terms. Read More

We generalize the method of computing functional determinants with excluded zero mode developed by McKane and Tarlie to the differential operators with degenerate zero modes. We consider a $2\times 2$ matrix differential operator with two independent zero modes and show that its functional determinant can be expressed only in terms of these modes in the spirit of Gel'fand-Yaglom approach. Our result can be easily extended to the case of $N\times N$ matrix differential operators with $N$ zero modes. Read More

We study spin chain analogs of the two-dimensional Kitaev honeycomb lattice model, which allows us to relate Anderson resonating valence bond states with superconductivity in an exact manner. In addition to their connection with p-wave superconductivity, such chains can be used for topological quantum computation as a result of the emergent Z_2 symmetry, as we show using Majorana fermions. We then focus on the problem of two coupled chains (ladders) : using Majorana fermions, we derive an analytical expression for the energy spectrum in the general case, which allows us to compare the square ladder and the honeycomb ribbon. Read More

We study the projective properties of planar zeros of tree-level scattering amplitudes in various theories. Whereas for pure scalar field theories we find that the planar zeros of the five-point amplitude do not enjoy projective invariance, coupling scalars to gauge fields gives rise to tree-level amplitudes whose planar zeros are determined by homogeneous polynomials in the stereographic coordinates labelling the direction of flight of the outgoing particles. In the case of pure gauge theories, this projective structure is generically destroyed if string corrections are taken into account. Read More

We conjecture a formula for the generating function of virtual $\chi_y$-genera of moduli spaces of rank 2 sheaves on minimal surfaces of general type. Specializing this conjecture to virtual Euler characteristics, we recover (part of) a formula of C. Vafa and E. Read More

We extend the idea of conformal attractors in inflation to non-canonical sectors by developing a non-canonical conformally invariant theory from two different approaches. In the first approach, namely, ${\cal N}=1$ supergravity, the construction is more or less phenomenological, where the non-canonical kinetic sector is derived from a particular form of the K$\ddot{a}$hler potential respecting shift symmetry. In the second approach i. Read More

A semi-classical analysis of backreaction in an expanding Universe with a conformally coupled scalar field and vacuum energy is presented. It is shown that a local observer perceives de Sitter space to contain a constant thermal energy density despite the dilution from expansion due to a continuous flux of energy radiated from the horizon. The self-consistent solution for the Hubble rate is found to be gradually evolving and at late times deviates significantly from de Sitter. Read More

In this paper we systematically construct simply transitive homogeneous spacetime solutions of the three-dimensional Minimal Massive Gravity (MMG) model. In addition to those that have analogs in Topologically Massive Gravity, such as warped AdS and pp-waves, there are several solutions genuine to MMG. Among them, there is a stationary Lifshitz metric with the dynamical exponent z=-1 and an anisotropic Lifshitz solution where all coordinates scale differently. Read More

Both classical and quantum waves can form vortices: with helical phase fronts and azimuthal current densities. These features determine the intrinsic orbital angular momentum carried by localized vortex states. In the past 25 years, optical vortex beams have become an inherent part of modern optics, with many remarkable achievements and applications. Read More