6 research outputs found
The Dressing Factor and Crossing Equations
We utilize the DHM integral representation for the BES dressing factor of the
world-sheet S-matrix of the AdS_5xS^5 light-cone string theory, and the
crossing equations to fix the principal branch of the dressing factor on the
rapidity torus. The results obtained are further used, in conjunction with the
fusion procedure, to determine the bound state dressing factor of the mirror
theory. We convincingly demonstrate that the mirror bound state S-matrix found
in this way does not depend on the internal structure of a bound state solution
employed in the fusion procedure. This welcome feature is in perfect parallel
to string theory, where the corresponding bound state S-matrix has no bearing
on bound state constituent particles as well. The mirror bound state S-matrix
we found provides the final missing piece in setting up the TBA equations for
the AdS_5xS^5 mirror theory.Comment: LaTex, 48 pages, 10 figures; v2: a new section added where the
dressing factor of the mirror theory is found; v3: formula (6.12) is
corrected, a new figure is added, accepted for publication in J.Phys.
Y-system for Scattering Amplitudes
We compute N=4 Super Yang Mills planar amplitudes at strong coupling by
considering minimal surfaces in AdS_5 space. The surfaces end on a null
polygonal contour at the boundary of AdS. We show how to compute the area of
the surfaces as a function of the conformal cross ratios characterizing the
polygon at the boundary. We reduce the problem to a simple set of functional
equations for the cross ratios as functions of the spectral parameter. These
equations have the form of Thermodynamic Bethe Ansatz equations. The area is
the free energy of the TBA system. We consider any number of gluons and in any
kinematic configuration.Comment: 69 pages, 19 figures, v2: references added, minor addition
Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
Moving from the mirror theory Bethe-Yang equations proposed by Arutyunov and
Frolov, we derive the thermodynamic Bethe Ansatz equations which should control
the spectrum of the planar correspondence. The
associated set of universal functional relations (Y-system) satisfied by the
exponentials of the TBA pseudoenergies is deduced, confirming the structure
inferred by Gromov, Kazakov and Vieira.Comment: Main typos corrected, notations fixed, references adde
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
Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang-Mills Theory: TBA and excited states
Using the thermodynamical Bethe ansatz method we derive an infinite set of
integral non-linear equations for the spectrum of states/operators in AdS/CFT.
The Y-system conjectured in arXiv:0901.3753 for the spectrum of all operators
in planar N=4 SYM theory follows from these equations. In particular, we
present the integral equations for the spectrum of all operators within the
sl(2) sector. We prove that all the kernels and free terms entering these TBA
equations are real and have nice fusion properties in the relevant mirror
kinematics. We find the analogue of DHM formula for the dressing kernel in the
mirror kinematics.Comment: Journal versio