arXiv subjects
Publications and source records attributed to Robert G. Leigh.
We compute directly the entanglement entropy of spatial regions in Chern-Simons gauge theories in 2+1 dimensions using surgery. We use these results to determine the universal topological piece of the entanglement entropy for Abelian and non-Abelian quantum Hall fluids.
In this note we discuss the wave functional approach to the spectrum of pure Yang-Mills theory in 2+1 and 3+1 dimensions by highlighting the issues of dynamical mass generation and the role played by the kinetic term. We extrapolate our recent analysis of 2+1 Yang-Mills theory to 3+1 dimensions, and under certain heuristic assumptions use a simple quasi-Gaussian vacuum wavefunctional for 3+1 Yang-Mills theory for a preliminary study of the spectrum of glueballs which nicely fits the available lattice simulations.
We discuss the implementation of electric-magnetic duality transformations in four-dimensional gravity linearized around Minkowski or (A)dS4 backgrounds. In the presence of a cosmological constant duality generically modifies the Hamiltonian, nevertheless the bulk dynamics is unchanged. We pay particular attention to the boundary terms generated by the duality transformations and discuss their implications for holography.
We present details of the analytic computation of the spectrum of lowest spin glueballs in pure Yang-Mills theory in 2+1 dimensions. The new ingredient is provided by the conjectured new non-trivial expression for the (quasi)Gaussian part of the ground state wave-functional. We show that this wave-functional can be derived by solving the Schrodinger equation under certain assumptions. The mass spectrum of the theory is determined by the zeros of Bessel functions, and the agreement with available lattice data is excellent.
We construct the low energy theory of a doped Mott insulator, such as the high-temperature superconductors, by explicitly integrating over the degrees of freedom far away from the chemical potential. For either hole or electron doping, a charge 2e bosonic field emerges at low energy. The charge 2e boson mediates dynamical spectral weight transfer across the Mott gap and creates a new charge e excitation by binding a hole. The result is a bifurcation of the electron dispersion below the chemical potential as observed recently in angle-resolved photoemission on Pb-doped Bi_2Sr_2CaCu_2O_{8+δ} (Pb2212).
We analytically compute the spectrum of the spin zero glueballs in the planar limit of pure Yang-Mills theory in 2+1 dimensions. The new ingredient is provided by our computation of a new non-trivial form of the ground state wave-functional. The mass spectrum of the theory is determined by the zeroes of Bessel functions, and the agreement with large N lattice data is excellent.
We discuss an analytic approach towards the solution of pure Yang-Mills theory in 3+1 dimensional spacetime. The approach is based on the use of local gauge invariant variables in the Schrödinger representation and the large $N$, planar limit. In particular, within this approach we point out unexpected parallels between pure Yang-Mills theory in 2+1 and 3+1 dimensions. The most important parallel shows up in the analysis of the ground state wave-functional especially in view of the numerical similarity of the existing large N lattice simulations of the spectra of 2+1 and 3+1 Yang Mills theories.
We consider the non-trivial boundary conformal field theory with exactly marginal boundary deformation. In recent years this deformation has been studied in the context of rolling tachyons and S-branes in string theory. Here we study the problem directly from an open string point of view, at one loop. We formulate the theory of the Z_2 reflection orbifold. To do so, we extend fermionization techniques originally introduced by Polchinski and Thorlacius. We also explain how to perform the open string computations at arbitrary (rational) radius, by consistently constructing the corresponding shift orbifold, and show in what sense these are related to known boundary states. In a companion paper, we use these results in a cosmological context involving decaying branes.
Unstable D-branes are central objects in string theory, and exist also in time-dependent backgrounds. In this paper we take first steps to studying brane decay in spacetime orbifolds. As a concrete model we focus on the R^{1,d}/Z_2 orbifold. We point out that on a spacetime orbifold there exist two kinds of S-branes, fractional S-branes in addition to the usual ones. We investigate their construction in the open string and closed string boundary state approach. As an application of these constructions, we consider a scenario where an unstable brane nucleates at the origin of time of a spacetime, its initial energy then converting into energy flux in the form of closed strings. The dual open string description allows for a well-defined description of this process even if it originates at a singular origin of the spacetime.
We present a novel scenario where matter in a spacetime originates from a decaying brane at the origin of time. The decay could be considered as a ``Big Bang''-like event at X^0=0. The closed string interpretation is a time-dependent spacetime with a semi-infinite time direction, with the initial energy of the brane converted into energy flux from the origin. The open string interpretation can be viewed as a string theoretic non-singular initial condition.
We study the large N (planar) limit of pure SU(N) 2+1 dimensional Yang-Mills theory (YM_{2+1}) using a gauge-invariant matrix parameterization introduced by Karabali and Nair. This formulation crucially relies on the properties of local holomorphic gauge invariant collective fields in the Hamiltonian formulation of YM_{2+1}. We show that the spectrum in the planar limit of this theory can be explicitly determined in the $N=\infty$, low momentum (large 't Hooft coupling) limit, using the technology of the Eguchi-Kawai reduction and the existing knowledge concerning the one-matrix model. The dispersion relation describing the planar YM_{2+1} spectrum reads as $ω(\vec{k}) = \sqrt{\vec{k}^2 + m_n^2}$, where $n=1,2,...$ and $m_n = n m_r$, where $m_r$ denotes the renormalized mass, the bare mass m being determined by the planar 't Hooft coupling $g_{YM}^2 N$ via $m= \frac{g_{YM}^2 N}{2 π}$. The planar, low momentum limit, also captures the expected short and long distance physics of YM_{2+1} and gives an interesting new picture of confinement. The computation of the spectrum is possible due to a reduction of the YM_{2+1} Hamiltonian for the large 't Hooft coupling to the {\it singlet} sector of an effective one matrix model. The crucial observation is that the correct vacuum (the large N master field), consistent with the area law and the existence of a mass gap, is described by an effective quadratic matrix model, in the large N, large 't Hooft coupling limit.
We consider a $R^{1,d}/Z_2$ orbifold, where $Z_2$ acts by time and space reversal, also known as the embedding space of the elliptic de Sitter space. The background has two potentially dangerous problems: time-nonorientability and the existence of closed time-like curves. We first show that closed causal curves disappear after a proper definition of the time function. We then consider the one-loop vacuum expectation value of the stress tensor. A naive QFT analysis yields a divergent result. We then analyze the stress tensor in bosonic string theory, and find the same result as if the target space would be just the Minkowski space $R^{1,d}$, suggesting a zero result for the superstring. This leads us to propose a proper reformulation of QFT, and recalculate the stress tensor. We find almost the same result as in Minkowski space, except for a potential divergence at the initial time slice of the orbifold, analogous to a spacelike Big Bang singularity. Finally, we argue that it is possible to define local S-matrices, even if the spacetime is globally time-nonorientable.
We show that there is a natural action of SL(2,Z) on the two-point functions of the energy momentum tensor and of higher-spin conserved currents in three-dimensional CFTs. The dynamics behind the S-operation of SL(2,Z) is that of an irrelevant current-current deformation and we point out its similarity to the dynamics of a wide class of three-dimensional CFTs. The holographic interpretation of our results raises the possibility that many three-dimensional CFTs have duals on AdS4 with SL(2,Z) duality properties at the linearized level.
Deconstruction provides a novel way of dealing with the notoriously difficult ultraviolet problems of four-dimensional gravity. This approach also naturally leads to a new perspective on the holographic principle, tying it to the fundamental requirements of unitarity and diffeomorphism invariance, as well as to a new viewpoint on the cosmological constant problem. The numerical smallness of the cosmological constant is implied by a unique combination of holography and supersymmetry, opening a new window into the fundamental physics of the vacuum.
It was recently pointed out that the physics of a single discrete gravitational extra dimension exhibits a peculiar UV/IR connection relating the UV scale to the radius of the effective extra dimension. Here we note that this non-locality is a manifestation of holography, encoding the correct scaling of the number of fundamental degrees of freedom of the UV theory. This in turn relates the Wilsonian RG flow in the UV theory to the effective gravitational dynamics in the extra dimension. The relevant holographic c-function is determined by the expression for the holographic bound. Holography in this context is a result of the requirements of unitarity and diffeomorphism invariance. We comment on the relevance of this observation for the cosmological constant problem.
Witten has presented an argument for the vanishing of the cosmological constant in 2+1 dimensions. This argument is crucially tied to the specific properties of (2+1)-dimensional gravity. We argue that this reasoning can be deconstructed to 3+1 dimensions under certain conditions. Our observation is also tied to a possibility that there exists a well-defined UV completion of (3+1)-dimensional gravity.
The quantum Hall system is known to have two mutually dual Chern-Simons descriptions, one associated with the hydrodynamics of the electron fluid, and another associated with the statistics. Recently, Susskind has made the claim that the hydrodynamic Chern-Simons theory should be considered to have a non-commutative gauge symmetry. The statistical Chern-Simons theory has a perturbative momentum expansion. In this paper, we study this perturbation theory and show that the effective action, although commutative at leading order, is non-commutative. This conclusion is arrived at through a careful study of the three-point function of Chern-Simons gauge fields. The non-commutative gauge symmetry of this system is thus a quantum symmetry, which we show can only be fully realized only through the inclusion of all orders in perturbation theory. We discuss the duality between the two non-commutative descriptions.
We consider aspects of holography in the $pp$-wave limit of $AdS_5\times S5$. This geometry contains two $\RR4$'s, one obtained from $AdS_5$ directions, and the other from the $S 5$. We argue that the holographic direction in the $pp$-wave background can be taken to be $r$, the radial direction in the first $\RR4 $. Normalizable modes correspond to states, and non-normalizable modes correspond to deformations of the boundary theory. In the strict $pp$-wave limit, there are additional non-normalizable modes in the second $\RR 4$, which have no apparent super-Yang-Mills interpretation. We outline the procedure for calculating correlation functions holographically.