The operator algebra of the discrete state operators in 2D gravity with non-vanishing cosmological constant

Remarks are given to the structure of physical states in 2D gravity coupled to $C\leq 1$ matter. The operator algebra of the discrete state operators is calculated for the theory with non-vanishing cosmological constant.Comment: 17 page

Wilson Loop Renormalization Group Flows

The locally BPS Wilson loop and the pure gauge Wilson loop map under AdS/CFT duality to string world-sheet boundaries with standard and alternate quantizations of the world-sheet fields. This implies an RG flow between the two operators, which we verify at weak coupling. Many additional loop operators exist at strong coupling, with a rich pattern of RG flows.Comment: 10 p, 2 figures. v3: Title change, expanded treatment of RG flow

Loop expansion in Yang-Mills thermodynamics

We argue that a selfconsistent spatial coarse-graining, which involves interacting (anti)calorons of unit topological charge modulus, implies that real-time loop expansions of thermodynamical quantities in the deconfining phase of SU(2) and SU(3) Yang-Mills thermodynamics are, modulo 1PI resummations, determined by a finite number of connected bubble diagrams.Comment: 15 pages, 2 figures, v5: discussion of much more severely constrained nonplanar situation included in Sec.

Rectangular Wilson Loops at Large N

This work is about pure Yang-Mills theory in four Euclidean dimensions with gauge group SU(N). We study rectangular smeared Wilson loops on the lattice at large N and relatively close to the large-N transition point in their eigenvalue density. We show that the string tension can be extracted from these loops but their dependence on shape differs from the asymptotic prediction of effective string theory.Comment: 47 pages, 21 figures, 8 table

Scale without Conformal Invariance at Three Loops

We carry out a three-loop computation that establishes the existence of scale without conformal invariance in dimensional regularization with the MS scheme in d=4-epsilon spacetime dimensions. We also comment on the effects of scheme changes in theories with many couplings, as well as in theories that live on non-conformal scale-invariant renormalization group trajectories. Stability properties of such trajectories are analyzed, revealing both attractive and repulsive directions in a specific example. We explain how our results are in accord with those of Jack & Osborn on a c-theorem in d=4 (and d=4-epsilon) dimensions. Finally, we point out that limit cycles with turning points are unlike limit cycles with continuous scale invariance.Comment: 21 pages, 3 figures, Erratum adde

On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT

We consider the 2-point function of string vertex operators representing string state with large spin in AdS_5. We compute this correlator in the semiclassical approximation and show that it has the expected (on the basis of state-operator correspondence) form of the strong-coupling limit of the 2-point function of single trace minimal twist operators in gauge theory. The semiclassical solution representing the stationary point of the path integral with two vertex operator insertions is found to be related to the large spin limit of the folded spinning string solution by a euclidean continuation, transformation to Poincare coordinates and conformal map from cylinder to complex plane. The role of the source terms coming from the vertex operator insertions is to specify the parameters of the solution in terms of quantum numbers (dimension and spin) of the corresponding string state. Understanding further how similar semiclassical methods may work for 3-point functions may shed light on strong-coupling limit of the corresponding correlators in gauge theory as was recently suggested by Janik et al in arXiv:1002.4613.Comment: 19 pages, 1 figure; minor corrections, references added, footnote below eq. (4.5) adde

Chiral Generations on Intersecting 5-branes in Heterotic String Theory

We show that there exist two 27 and one 27 bar of E6, net one D=4, N=1 chiral matter supermultiplet as zero modes localized on the intersection of two 5-branes in the E8 x E8 heterotic string theory. The smeared intersecting 5-brane solution is used via the standard embedding to construct a heterotic background, which provides, after a compactification of some of the transverse dimensions, a five-dimensional Randall-Sundrum II like brane-world set-up in heterotic string theory. As a by-product, we present a new proof of anomaly cancellation between those from the chiral matter and the anomaly inflow onto the brane without small instanton.Comment: 26 pages, 5 figures; references added, typo correcte

Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory

We present a study of the free energy of parameterized Polyakov loops P in SU(2) and SU(3) lattice gauge theory as a function of the parameters that characterize P. We explore temperatures below and above the deconfinement transition, and for our highest temperatures T > 5 T_c we compare the free energy to perturbative results.Comment: Minor changes. Final version to appear in JHE