Wrapping corrections for non-diagonal boundaries in AdS/CFT

We consider an open string stretched between a Y=0 brane and a Y_theta=0 brane. The latter brane is rotated with respect to the former by an angle theta, and is described by a non-diagonal boundary S-matrix. This system interpolates smoothly between the Y-Y (theta =0) and the Y-bar Y (theta = pi/2) systems, which are described by diagonal boundary S-matrices. We use integrability to compute the energies of one-particle states at weak coupling up to leading wrapping order (4, 6 loops) as a function of the angle. The results for the diagonal cases exactly match with those obtained previously.Comment: 21 pages, 1 figur

NLIE for hole excited states in the sine-Gordon model with two boundaries

We derive a nonlinear integral equation (NLIE) for some bulk excited states of the sine-Gordon model on a finite interval with general integrable boundary interactions, including boundary terms proportional to the first time derivative of the field. We use this NLIE to compute numerically the dimensions of these states as a function of scale, and check the UV and IR limits analytically. We also find further support for the ground-state NLIE by comparison with boundary conformal perturbation theory (BCPT), boundary truncated conformal space approach (BTCSA) and the boundary analogue of the Luscher formula.Comment: 31 pages, LaTeX; graphicx, epstopdf, 4 figure

Geometry of W-algebras from the affine Lie algebra point of view

To classify the classical field theories with W-symmetry one has to classify the symplectic leaves of the corresponding W-algebra, which are the intersection of the defining constraint and the coadjoint orbit of the affine Lie algebra if the W-algebra in question is obtained by reducing a WZNW model. The fields that survive the reduction will obey non-linear Poisson bracket (or commutator) relations in general. For example the Toda models are well-known theories which possess such a non-linear W-symmetry and many features of these models can only be understood if one investigates the reduction procedure. In this paper we analyze the SL(n,R) case from which the so-called W_n-algebras can be obtained. One advantage of the reduction viewpoint is that it gives a constructive way to classify the symplectic leaves of the W-algebra which we had done in the n=2 case which will correspond to the coadjoint orbits of the Virasoro algebra and for n=3 which case gives rise to the Zamolodchikov algebra. Our method in principle is capable of constructing explicit representatives on each leaf. Another attractive feature of this approach is the fact that the global nature of the W-transformations can be explicitly described. The reduction method also enables one to determine the ``classical highest weight (h. w.) states'' which are the stable minima of the energy on a W-leaf. These are important as only to those leaves can a highest weight representation space of the W-algebra be associated which contains a ``classical h. w. state''.Comment: 17 pages, LaTeX, revised 1. and 7. chapter

The spectrum of tachyons in AdS/CFT

We analyze the spectrum of open strings stretched between a D-brane and an anti-D-brane in planar AdS/CFT using various tools. We focus on open strings ending on two giant gravitons with different orientation in $AdS_5 \times S^5$ and study the spectrum of string excitations using the following approaches: open spin-chain, boundary asymptotic Bethe ansatz and boundary thermodynamic Bethe ansatz (BTBA). We find agreement between a perturbative high order diagrammatic calculation in ${\cal N}=4$ SYM and the leading finite-size boundary Luscher correction. We study the ground state energy of the system at finite coupling by deriving and numerically solving a set of BTBA equations. While the numerics give reasonable results at small coupling, they break down at finite coupling when the total energy of the string gets close to zero, possibly indicating that the state turns tachyonic. The location of the breakdown is also predicted analytically.Comment: 40 pages, lots of figures, v2: typos corrected, accepted for publication in JHE

Minimal model boundary flows and c=1 CFT

We consider perturbations of unitary minimal models by boundary fields. Initially we consider the models in the limit as c -> 1 and find that the relevant boundary fields all have simple interpretations in this limit. This interpretation allows us to conjecture the IR limits of flows in the unitary minimal models generated by the fields \phi_{rr} of `low' weight. We check this conjecture using the truncated conformal space approach. In the process we find evidence for a new series of integrable boundary flows.Comment: (latex2e, 27 pages, 17 figures

Casimir effect in the boundary state formalism

Casimir effect in the planar setting is described using the boundary state formalism, for general partially reflecting boundaries. It is expressed in terms of the low-energy degrees of freedom, which provides a large distance expansion valid for general interacting field theories provided there is a non-vanishing mass gap. The expansion is written in terms of the scattering amplitudes, and needs no ultraviolet renormalization. We also discuss the case when the quantum field has a nontrivial vacuum configuration.Comment: 11 pages. Proceedings contribution of talk given at the Workshop on Quantum Field Theory under the Influence of External Conditions (QFEXT07), University of Leipzig, September 16-21, 2007. To appear in J. Phys.

The sine-Gordon model with integrable defects revisited

Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditions on the defect point consistent with Liouville integrability.Comment: 24 pages Latex. Minor modifications, added comment

TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT

The ground-state energy of integrably-twisted theories is analyzed in finite volume. We derive the leading and next-to-leading order (NLO) L\"uscher-type corrections for large volumes of the vacuum energy for integrable theories with twisted boundary conditions and twisted S-matrix. We then derive the twisted thermodynamic Bethe ansatz (TBA) equations to describe exactly the ground state, from which we obtain an untwisted Y-system. The two approaches are compared by expanding the TBA equations to NLO, and exact agreement is found. We give explicit results for the O(4) model and for the three-parameter family of $\gamma$-deformed (non-supersymmetric) planar AdS/CFT model, where the ground-state energy can be nontrivial and can acquire finite-size corrections. The NLO corrections, which correspond to double-wrapping diagrams, are explicitly evaluated for the latter model at six loops.Comment: 42 pages, 2 figures, v2: references added, v3: minor correction

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