Boundary operators in minimal Liouville gravity and matrix models

We interpret the matrix boundaries of the one matrix model (1MM) recently constructed by two of the authors as an outcome of a relation among FZZT branes. In the double scaling limit, the 1MM is described by the (2,2p+1) minimal Liouville gravity. These matrix operators are shown to create a boundary with matter boundary conditions given by the Cardy states. We also demonstrate a recursion relation among the matrix disc correlator with two different boundaries. This construction is then extended to the two matrix model and the disc correlator with two boundaries is compared with the Liouville boundary two point functions. In addition, the realization within the matrix model of several symmetries among FZZT branes is discussed.Comment: 26 page

Correlation Functions in 2-Dimensional Integrable Quantum Field Theories

In this talk I discuss the form factor approach used to compute correlation functions of integrable models in two dimensions. The Sinh-Gordon model is our basic example. Using Watson's and the recursive equations satisfied by matrix elements of local operators, I present the computation of the form factors of the elementary field $\phi(x)$ and the stress-energy tensor $T_{\mu\nu}(x)$ of the theory.Comment: 19pp, LATEX version, (talk at Como Conference on ``Integrable Quantum Field Theories''

One-point functions in massive integrable QFT with boundaries

We consider the expectation value of a local operator on a strip with non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite volume regularisation in the crossed channel and extending the boundary state formalism to the finite volume case we give a series expansion for the one-point function in terms of the exact form factors of the theory. The truncated series is compared with the numerical results of the truncated conformal space approach in the scaling Lee-Yang model. We discuss the relevance of our results to quantum quench problems.Comment: 43 pages, 20 figures, v2: typos correcte

Conformal symmetry in non-local field theories

We have shown that a particular class of non-local free field theory has conformal symmetry in arbitrary dimensions. Using the local field theory counterpart of this class, we have found the Noether currents and Ward identities of the translation, rotation and scale symmetries. The operator product expansion of the energy-momentum tensor with quasi-primary fields is also investigated.Comment: 15 pages, V2 (Some references added) V3(published version

Bounds for State Degeneracies in 2D Conformal Field Theory

In this note we explore the application of modular invariance in 2-dimensional CFT to derive universal bounds for quantities describing certain state degeneracies, such as the thermodynamic entropy, or the number of marginal operators. We show that the entropy at inverse temperature 2 pi satisfies a universal lower bound, and we enumerate the principal obstacles to deriving upper bounds on entropies or quantum mechanical degeneracies for fully general CFTs. We then restrict our attention to infrared stable CFT with moderately low central charge, in addition to the usual assumptions of modular invariance, unitarity and discrete operator spectrum. For CFT in the range c_left + c_right < 48 with no relevant operators, we are able to prove an upper bound on the thermodynamic entropy at inverse temperature 2 pi. Under the same conditions we also prove that a CFT can have a number of marginal deformations no greater than ((c_left + c_right) / (48 - c_left - c_right)) e^(4 Pi) - 2.Comment: 23 pages, LaTeX, minor change

On the crossing relation in the presence of defects

The OPE of local operators in the presence of defect lines is considered both in the rational CFT and the $c>25$ Virasoro (Liouville) theory. The duality transformation of the 4-point function with inserted defect operators is explicitly computed. The two channels of the correlator reproduce the expectation values of the Wilson and 't Hooft operators, recently discussed in Liouville theory in relation to the AGT conjecture.Comment: TEX file with harvmac; v3: JHEP versio

Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations

We discuss designer Hamiltonians---lattice models tailored to be free from sign problems ("de-signed") when simulated with quantum Monte Carlo methods but which still host complex many-body states and quantum phase transitions of interest in condensed matter physics. We focus on quantum spin systems in which competing interactions lead to non-magnetic ground states. These states and the associated quantum phase transitions can be studied in great detail, enabling direct access to universal properties and connections with low-energy effective quantum field theories. As specific examples, we discuss the transition from a Neel antiferromagnet to either a uniform quantum paramagnet or a spontaneously symmetry-broken valence-bond solid in SU(2) and SU(N) invariant spin models. We also discuss anisotropic (XXZ) systems harboring topological Z2 spin liquids and the XY* transition. We briefly review recent progress on quantum Monte Carlo algorithms, including ground state projection in the valence-bond basis and direct computation of the Renyi variants of the entanglement entropy.Comment: 23 pages, 10 figure

Conformal Invariance in Percolation, Self-Avoiding Walks and Related Problems

Over the years, problems like percolation and self-avoiding walks have provided important testing grounds for our understanding of the nature of the critical state. I describe some very recent ideas, as well as some older ones, which cast light both on these problems themselves and on the quantum field theories to which they correspond. These ideas come from conformal field theory, Coulomb gas mappings, and stochastic Loewner evolution.Comment: Plenary talk given at TH-2002, Paris. 21 pages, 9 figure

Bekenstein entropy bound for weakly-coupled field theories on a 3-sphere

We calculate the high temperature partition functions for SU(Nc) or U(Nc) gauge theories in the deconfined phase on S^1 x S^3, with scalars, vectors, and/or fermions in an arbitrary representation, at zero 't Hooft coupling and large Nc, using analytical methods. We compare these with numerical results which are also valid in the low temperature limit and show that the Bekenstein entropy bound resulting from the partition functions for theories with any amount of massless scalar, fermionic, and/or vector matter is always satisfied when the zero-point contribution is included, while the theory is sufficiently far from a phase transition. We further consider the effect of adding massive scalar or fermionic matter and show that the Bekenstein bound is satisfied when the Casimir energy is regularized under the constraint that it vanishes in the large mass limit. These calculations can be generalized straightforwardly for the case of a different number of spatial dimensions.Comment: 32 pages, 12 figures. v2: Clarifications added. JHEP versio

Limit Cycles and Conformal Invariance

There is a widely held belief that conformal field theories (CFTs) require zero beta functions. Nevertheless, the work of Jack and Osborn implies that the beta functions are not actually the quantites that decide conformality, but until recently no such behavior had been exhibited. Our recent work has led to the discovery of CFTs with nonzero beta functions, more precisely CFTs that live on recurrent trajectories, e.g., limit cycles, of the beta-function vector field. To demonstrate this we study the S function of Jack and Osborn. We use Weyl consistency conditions to show that it vanishes at fixed points and agrees with the generator Q of limit cycles on them. Moreover, we compute S to third order in perturbation theory, and explicitly verify that it agrees with our previous determinations of Q. A byproduct of our analysis is that, in perturbation theory, unitarity and scale invariance imply conformal invariance in four-dimensional quantum field theories. Finally, we study some properties of these new, "cyclic" CFTs, and point out that the a-theorem still governs the asymptotic behavior of renormalization-group flows.Comment: 31 pages, 4 figures. Expanded introduction to make clear that cycles discussed in this work are not associated with unitary theories that are scale but not conformally invarian