510 research outputs found
On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function
We investigate the sub-leading contributions to the free energy of Bethe
Ansatz solvable (continuum) models with different boundary conditions. We show
that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1)
pieces if both the density of states in rapidity space and the quadratic
fluctuations around the saddle point solution to the TBA are properly taken
into account. In relativistic boundary QFT the O(1) contributions are directly
related to the exact g-function. In this paper we provide an all-orders proof
of the previous results of P. Dorey et al. on the g-function in both massive
and massless models. In addition, we derive a new result for the g-function
which applies to massless theories with arbitrary diagonal scattering in the
bulk.Comment: 28 pages, 2 figures, v2: minor corrections, v3: minor corrections and
references adde
Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms
The standard numerical approach to determining matrix elements of local
operators and width of resonances uses the finite volume dependence of energy
levels and matrix elements. Finite size corrections that decay exponentially in
the volume are usually neglected or taken into account using perturbation
expansion in effective field theory. Using two-dimensional sine-Gordon field
theory as "toy model" it is shown that some exponential finite size effects
could be much larger than previously thought, potentially spoiling the
determination of matrix elements in frameworks such as lattice QCD. The
particular class of finite size corrections considered here are mu-terms
arising from bound state poles in the scattering amplitudes. In sine-Gordon
model, these can be explicitly evaluated and shown to explain the observed
discrepancies to high precision. It is argued that the effects observed are not
special to the two-dimensional setting, but rather depend on general field
theoretic features that are common with models relevant for particle physics.
It is important to understand these finite size corrections as they present a
potentially dangerous source of systematic errors for the determination of
matrix elements and resonance widths.Comment: 26 pages, 13 eps figures, LaTeX2e fil
Solving the Simplest Theory of Quantum Gravity
We solve what is quite likely the simplest model of quantum gravity, the
worldsheet theory of an infinitely long, free bosonic string in Minkowski
space. Contrary to naive expectations, this theory is non-trivial. We
illustrate this by constructing its exact factorizable S-matrix. Despite its
simplicity, the theory exhibits many of the salient features expected from more
mature quantum gravity models, including the absence of local off-shell
observables, a minimal length, a maximum achievable (Hagedorn) temperature, as
well as (integrable relatives of) black holes. All these properties follow from
the exact S-matrix. We show that the complete finite volume spectrum can be
reconstructed analytically from this S-matrix with the help of the
thermodynamic Bethe Ansatz. We argue that considered as a UV complete
relativistic two-dimensional quantum field theory the model exhibits a new type
of renormalization group flow behavior, "asymptotic fragility". Asymptotically
fragile flows do not originate from a UV fixed point.Comment: 32+4 pages, 1 figure, v2: typos fixed, published versio
Large N and Bosonization in Three Dimensions
Bosonization is normally thought of as a purely two-dimensional phenomenon,
and generic field theories with fermions in D>2 are not expected be describable
by local bosonic actions, except in some special cases. We point out that 3D
SU(N) gauge theories on R^{1,1} x S^{1}_{L} with adjoint fermions can be
bosonized in the large N limit. The key feature of such theories is that they
enjoy large N volume independence for arbitrary circle size L. A consequence of
this is a large N equivalence between these 3D gauge theories and certain 2D
gauge theories, which matches a set of correlation functions in the 3D theories
to corresponding observables in the 2D theories. As an example, we focus on a
3D SU(N) gauge theory with one flavor of adjoint Majorana fermions and derive
the large-N equivalent 2D gauge theory. The extra dimension is encoded in the
color degrees of freedom of the 2D theory. We then apply the technique of
non-Abelian bosonization to the 2D theory to obtain an equivalent local theory
written purely in terms of bosonic variables. Hence the bosonized version of
the large N three-dimensional theory turns out to live in two dimensions.Comment: 30 pages, 2 tables. v2 minor revisions, references adde
Quantum finite-size effects for dyonic magnons in the AdS_4 x CP^3
We compute quantum corrections to finite-size effects for various dyonic
giant magnons in the AdS_4 x CP^3 in two different approaches. The off-shell
algebraic curve method is used to quantize the classical string configurations
in semi-classical way and to compute the corrections to the string energies.
These results are compared with the F-term L\"uscher formula based on the
S-matrix of the AdS_4 / CFT_3. The fact that the two results match exactly
provides another stringent test for the all-loop integrability conjecture and
the exact S-matrix based on it.Comment: 21 pages, No figures, corrected typos, added some reference
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
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 -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
g-Functions and gluon scattering amplitudes at strong coupling
We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills
theory at strong coupling by calculating the area of the minimal surfaces in
AdS_3 based on the associated thermodynamic Bethe ansatz system. The remainder
function of the amplitudes is computed by evaluating the free energy, the T-
and Y-functions of the homogeneous sine-Gordon model. Using conformal field
theory (CFT) perturbation, we examine the mass corrections to the free energy
around the CFT point corresponding to the regular polygonal Wilson loop. Based
on the equivalence between the T-functions and the g-functions, which measure
the boundary entropy, we calculate corrections to the T- and Y-functions as
well as express them at the CFT point by the modular S-matrix. We evaluate the
remainder function around the CFT point for 8 and 10-point amplitudes
explicitly and compare these analytic expressions with the 2-loop formulas. The
two rescaled remainder functions show very similar power series structures.Comment: 51 pages, 4 figures, v2: some comments and references added, based on
the published version, v3: minor change
Moduli space coordinates and excited state g-functions
We consider the space of boundary conditions of Virasoro minimal models
formed from the composition of a collection of flows generated by \phi_{1,3}.
These have recently been shown to fall naturally into a sequence, each term
having a coordinate on it in terms of a boundary parameter, but no global
parameter has been proposed. Here we investigate the idea that the overlaps of
particular bulk states with the boundary states give natural coordinates on the
moduli space of boundary conditions. We find formulae for these overlaps using
the known thermodynamic Bethe Ansatz descriptions of the ground and first
excited state on the cylinder and show that they give a global coordinate on
the space of boundary conditions, showing it is smooth and compact as expected.Comment: 10 pages, 4 figure
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