Theta Dependence In The Large N Limit Of Four-Dimensional Gauge Theories

The theta dependent of pure gauge theories in four dimensions can be studied using a duality of large N gauge theories with string theory on a certain spacetime. Via this duality, one can argue that for every theta, there are infinitely many vacua that are stable in the large N limit. The true vacuum, found by minimizing the energy in this family, is a smooth function of theta except at theta equal to pi, where it jumps. This jump is associated with spontaneous breaking of CP symmetry. Domain walls separating adjacent vacua are described in terms of wrapped sixbranes.Comment: 8 p

Mirror Symmetry of Calabi-Yau Supermanifolds

We study super Landau-Ginzburg mirrors of the weighted projective superspace WCP^{3|2} which is a Calabi-Yau supermanifold and appeared in hep-th/0312171(Witten) in the topological B-model. One of them is an elliptic fibration over the complex plane whose coordinate is given in terms of two bosonic and two fermionic variables as well as Kahler parameter of WCP^{3|2}. The other is some patch of a degree 3 Calabi-Yau hypersurface in CP^2 fibered by the complex plane whose coordinate depends on both above four variables and Kahler parameter but its dependence behaves quite differently.Comment: 12pp; the last paragraph of section 1 improved and some clarifications adde

Loop Variables and Gauge Invariance in (Open) Bosonic String Theory

We give a simplified and more complete description of the loop variable approach for writing down gauge invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of loop variables, the interacting equations look exactly like the free equations, but with a loop variable depending on an extra parameter, thus making it a band of finite width. The arguments for gauge invariance work exactly as in the free case. We show that these equations are Wilsonian RG equations with a finite world-sheet cutoff and that in the infrared limit, equivalence with the Callan-Symanzik $\beta$-functions should ensure that they reproduce the on-shell scattering amplitudes in string theory. It is applied to the tachyon-photon system and the general arguments for gauge invariance can be easily checked to the order calculated. One can see that when there is a finite world sheet cutoff in place, even the U(1) invariance of the equations for the photon, involves massive mode contributions. A field redefinition involving the tachyon is required to get the gauge transformations of the photon into standard form.Comment: 20 pages, Late

Addendum to "Classical and Quantum Evolutions of the de Sitter and the anti-de Sitter Universes in 2+1 dimensions"

The previous discussion \cite{ezawa} on reducing the phase space of the first order Einstein gravity in 2+1 dimensions is reconsidered. We construct a \lq\lq correct" physical phase space in the case of positive cosmological constant, taking into account the geometrical feature of SO(3,1) connections. A parametrization which unifies the two sectors of the physical phase space is also given.Comment: Latex 8 pages (Crucial and essential changes have been made.

Conserved Linking in Single- and Double-Stranded Polymers

We demonstrate a variant of the Bond Fluctuation lattice Monte Carlo model in which moves through cis conformations are forbidden. Ring polymers in this model have a conserved quantity that amounts to a topological linking number. Increased linking number reduces the radius of gyration mildly. A linking number of order 0.2 per bond leads to an eight-percent reduction of the radius for 128-bond chains. This percentage appears to rise with increasing chain length, contrary to expectation. For ring chains evolving without the conservation of linking number, we demonstrate a substantial anti-correlation between the twist and writhe variables whose sum yields the linking number. We raise the possibility that our observed anti-correlations may have counterparts in the most important practical polymer that conserves linking number, DNA.Comment: Revised title, minor changes, updated references. 36 pages, including 14 figures. More formats available at http://rainbow.uchicago.edu/~plewa/webpaper

Distortion of Schwarzschild-anti-de Sitter black holes to black strings

Motivated by the existence of black holes with various topologies in four-dimensional spacetimes with a negative cosmological constant, we study axisymmetric static solutions describing any large distortions of Schwarzschild-anti-de Sitter black holes parametrized by the mass $m$. Under the approximation such that $m$ is much larger than the anti-de Sitter radius, it is found that a cylindrically symmetric black string is obtained as a special limit of distorted spherical black holes. Such a prolonged distortion of the event horizon connecting a Schwarzschild-anti-de Sitter black hole to a black string is allowed without violating both the usual black hole thermodynamics and the hoop conjecture for the horizon circumference.Comment: 13 pages, accepted for publication in Physical Review

Non-abelian gauge antisymmetric tensor fields

We construct the theory of non-abelian gauge antisymmetric tensor fields, which generalize the standard Yang-MIlls fields and abelian gauge p-forms. The corresponding gauge group acts on the space of inhomogeneous differential forms and it is shown to be a supergroup. The wide class of generalized Chern-Simons actions is constructed.Comment: 20 pages, Late

Schwarzschild-anti de Sitter within an Isothermal Cavity: Thermodynamics, Phase Transitions and the Dirichlet Problem

The thermodynamics of Schwarzschild black holes within an isothermal cavity and the associated Euclidean Dirichlet boundary-value problem are studied for four and higher dimensions in anti-de Sitter (AdS) space. For such boundary conditions classically there always exists a unique hot AdS solution and two or no Schwarzschild-AdS black-hole solutions depending on whether or not the temperature of the cavity-wall is above a minimum value, the latter being a function of the radius of the cavity. Assuming the standard area-law of black-hole entropy, it was known that larger and smaller holes have positive and negative specific heats and hence are locally thermodynamically stable and unstable respectively. In this paper we present the first derivation of this by showing that the standard area law of black-hole entropy holds in the semi-classical approximation of the Euclidean path integral for such boundary conditions. We further show that for wall-temperatures above a critical value a phase transition takes hot AdS to the larger Schwarzschild-AdS within the cavity. The larger hole thus can be globally thermodynamically stable above this temperature. The phase transition can occur for a cavity of arbitrary radius above a (corresponding) critical temperature. In the infinite cavity limit this picture reduces to that considered by Hawking and Page. The case of five dimensions is found to be rather special since exact analytic expressions can be obtained for the masses of the two holes as functions of cavity radius and temperature thus solving exactly the Euclidean Dirichlet problem. This makes it possible to compute the on-shell Euclidean action as functions of them from which other quantities of interest can be evaluated exactly.Comment: 23 pages, Late

Spinning flavour branes and fermion pairing instabilities

We consider probe Dp-branes, p=3,5,7, in global AdS_5 x S^5, rotating along an internal direction in the S^5. These are dual to strongly interacting N=4 SYM on S^3 with massless fundamental flavours, in the presence of an R-symmetry chemical potential for flavour fermions. For massless, "AdS-filling" Dp-brane embeddings at zero temperature, we find an infinite set of threshold values of the chemical potential at which instabilities are triggered. The onset of instability is always preceded by metastability of the zero density state. From the onset values of the chemical potential, we infer that unstable directions favour a homogeneous condensate of a bilinear made from fermion harmonics, or Cooper pairing. We confirm this picture both numerically and analytically. The linearized analysis showing the appearance of instabilities involves a charged scalar in global AdS space coupled to a (large) constant background gauge potential. The resulting frequency space correlator of the fermion bilinear at strong coupling displays poles in the upper half plane. In contrast, the correlator at zero coupling exhibits Pauli blocking due to occupation of states below the Fermi level, but no instabilities. The end-point of the strong coupling instability is not visible in our setup.Comment: 44 pages, 10 figures, uses late

Heavy Quark Potentials in Some Renormalization Group Revised AdS/QCD Models

We construct some AdS/QCD models by the systematic procedure of GKN. These models reflect three rather different asymptotics the gauge theory beta functions approach at the infrared region, $\beta\propto-\lambda^2, -\lambda^3$ and $\beta\propto-\lambda$, where $\lambda$ is the 't Hooft coupling constant. We then calculate the heavy quark potentials in these models by holographic methods and find that they can more consistently fit the lattice data relative to the usual models which do not include the renormalization group improving effects. But only use the lattice QCD heavy quark potentials as constrains, we cannot distinguish which kind of infrared asymptotics is the better one.Comment: comparisons with lattice results, qualitative consideration of quantum corrections are added. (accepted by Phys. Rev. D