17 research outputs found
Bound State Transfer Matrix for AdS5 x S5 Superstring
We apply the algebraic Bethe ansatz technique to compute the eigenvalues of
the transfer matrix constructed from the general bound state S-matrix of the
light-cone AdS5 x S5 superstring. This allows us to verify certain conjectures
on the quantum characteristic function, and to extend them to the general case.Comment: 36 pages, LaTeX, v2: typos corrected, ref added; v3: accepted for
publication in JHEP
The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
We derive a set of integral equations of the TBA type for the generalized
cusp anomalous dimension, or the quark antiquark potential on the three sphere,
as a function of the angles. We do this by considering a family of local
operators on a Wilson loop with charge L. In the large L limit the problem can
be solved in terms of a certain boundary reflection matrix. We determine this
reflection matrix by using the symmetries and the boundary crossing equation.
The cusp is introduced through a relative rotation between the two boundaries.
Then the TBA trick of exchanging space and time leads to an exact equation for
all values of L. The L=0 case corresponds to the cusped Wilson loop with no
operators inserted. We then derive a slightly simplified integral equation
which describes the small angle limit. We solve this equation up to three loops
in perturbation theory and match the results that were obtained with more
direct approaches.Comment: 63 pages, 12 figures. v2: references added, typos correcte
Konishi operator at intermediate coupling
TBA equations for two-particle states from the sl(2) sector proposed by
Arutyunov, Suzuki and the author are solved numerically for the Konishi
operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained
is used to analyze the properties of Y-functions and address the issue of the
existence of the critical values of the coupling. In addition we find a new
integral representation for the BES dressing phase which substantially reduces
the computational time.Comment: lots of figures, v2: improved numerics, c1=2, c2=0, c4 does not
vanis
T-systems and Y-systems in integrable systems
The T and Y-systems are ubiquitous structures in classical and quantum
integrable systems. They are difference equations having a variety of aspects
related to commuting transfer matrices in solvable lattice models, q-characters
of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras
with coefficients, periodicity conjectures of Zamolodchikov and others,
dilogarithm identities in conformal field theory, difference analogue of
L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem,
AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace
sequence in discrete geometry, Fermionic character formulas and combinatorial
completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics,
analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and
so forth. This review article is a collection of short reviews on these topics
which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5,
eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical
review) also needs these correction
T-system on T-hook : Grassmannian solution and twisted Quantum Spectral Curve
International audienceWe propose an efficient grassmannian formalism for solution of bi-linear finite-difference Hirota equation (T-system) on T-shaped lattices related to the space of highest weight representations of superalgebra. The formalism is inspired by the quantum fusion procedure known from the integrable spin chains and is based on exterior forms of Baxter-like Q-functions. We find a few new interesting relations among the exterior forms of Q-functions and reproduce, using our new formalism, the Wronskian determinant solutions of Hirota equations known in the literature. Then we generalize this construction to the twisted Q-functions and demonstrate the subtleties of untwisting procedure on the examples of rational quantum spin chains with twisted boundary conditions. Using these observations, we generalize the recently discovered, in our paper with N. Gromov, AdS/CFT Quantum Spectral Curve for exact planar spectrum of AdS/CFT duality to the case of arbitrary Cartan twisting of string sigma model. Finally, we successfully probe this formalism by reproducing the energy of gamma-twisted BMN vacuum at single-wrapping orders of weak coupling expansion