23 research outputs found
Three dimensional four-fermion models - A Monte Carlo study
We present results from numerical simulations of three different 3d
four-fermion models that exhibit Z_2, U(1), and SU(2) x SU(2) chiral
symmetries, respectively. We performed the simulations by using the hybrid
Monte Carlo algorithm. We employed finite size scaling methods on lattices
ranging from 8^3 to 40^3 to study the properties of the second order chiral
phase transition in each model. The corresponding critical coupling defines an
ultraviolet fixed point of the renormalization group. In our high precision
simulations, we detected next-to-leading order corrections for various critical
exponents and we found them to be in good agreement with existing analytical
large-N_f calculations.Comment: 15 pages, 7 figures, and 2 table
Noncompact SL(2,R) spin chain
We consider the integrable spin chain model - the noncompact SL(2,R) spin
magnet. The spin operators are realized as the generators of the unitary
principal series representation of the SL(2,R) group. In an explicit form, we
construct R-matrix, the Baxter Q-operator and the transition kernel to the
representation of the Separated Variables (SoV). The expressions for the energy
and quasimomentum of the eigenstates in terms of the Baxter Q-operator are
derived. The analytic properties of the eigenvalues of the Baxter operator as a
function of the spectral parameter are established. Applying the diagrammatic
approach, we calculate Sklyanin's integration measure in the separated
variables and obtain the solution to the spectral problem for the model in
terms of the eigenvalues of the Q-operator. We show that the transition kernel
to the SoV representation is factorized into a product of certain operators
each depending on a single separated variable.Comment: 29 pages, 12 figure
Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
We construct the Baxter Q-operator and the representation of the Separated
Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the
diagrammatical approach, we calculate Sklyanin's integration measure in the
separated variables and obtain the solution to the spectral problem for the
model in terms of the eigenvalues of the Q-operator. We show that the
transition kernel to the SoV representation is factorized into the product of
certain operators each depending on a single separated variable. As a
consequence, it has a universal pyramid-like form that has been already
observed for various quantum integrable models such as periodic Toda chain,
closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl
Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
Recently, several multi-loop conjectures have been proposed for the spin
dependence of anomalous dimensions of twist-2 and 3 operators in the sl(2)
sector of N=4 SYM. Currently, these conjectures are not proven, although
several consistency checks have been performed on their large spin expansion.
In this paper, we show how these expansions can be efficiently computed without
resorting to any conjecture. To this aim we present in full details a method to
expand at large spin the solution of the long-range Baxter equation. We treat
the twist-2 and 3 cases at two loops and the twist-3 case at three loops.
Several subtleties arise whose resolution leads to a simple algorithm computing
the expansion.Comment: 26 page
Colored Spin Systems, BKP Evolution and finite N_c effects
Even within the framework of the leading logarithmic approximation the
eigenvalues of the BKP kernel for states of more than three reggeized gluons
are unknown in general, contrary to the planar limit case where the problem
becomes integrable. We consider a 4-gluon kernel for a finite number of colors
and define some simple toy models for the configuration space dynamics, which
are directly solvable with group theoretical methods. Then we study the
dependence of the spectrum of these models with respect to the number of colors
and make comparisons with the large limit case.Comment: 17 pages, 4 figures, references update, to appear on EPJ
Separation of variables for the quantum SL(2,R) spin chain
We construct representation of the Separated Variables (SoV) for the quantum
SL(2,R) Heisenberg closed spin chain and obtain the integral representation for
the eigenfunctions of the model. We calculate explicitly the Sklyanin measure
defining the scalar product in the SoV representation and demonstrate that the
language of Feynman diagrams is extremely useful in establishing various
properties of the model. The kernel of the unitary transformation to the SoV
representation is described by the same "pyramid diagram" as appeared before in
the SoV representation for the SL(2,C) spin magnet. We argue that this kernel
is given by the product of the Baxter Q-operators projected onto a special
reference state.Comment: 26 pages, Latex style, 9 figures. References corrected, minor
stylistic changes, version to be publishe
Parton interactions in the Bjorken limit of QCD
We consider the Bjorken limit in the framework of the effective action
approach and discuss its similarities to the Regge limit. The proposed
effective action allows for a rather simple calculation of the known evolution
kernels. We represent the result in terms of two-parton interaction operators
involving gluon and quark operators depending on light-ray position and
helicity and analyze their symmetry properties.Comment: 32 pages LaTex, 4 eps-figures, comments added, minor correction
High Energy QCD: Stringy Picture from Hidden Integrability
We discuss the stringy properties of high-energy QCD using its hidden
integrability in the Regge limit and on the light-cone. It is shown that
multi-colour QCD in the Regge limit belongs to the same universality class as
superconformal =2 SUSY YM with at the strong coupling
orbifold point. The analogy with integrable structure governing the low energy
sector of =2 SUSY gauge theories is used to develop the brane picture
for the Regge limit. In this picture the scattering process is described by a
single M2 brane wrapped around the spectral curve of the integrable spin chain
and unifying hadrons and reggeized gluons involved in the process. New
quasiclassical quantization conditions for the complex higher integrals of
motion are suggested which are consistent with the duality of the
multi-reggeon spectrum. The derivation of the anomalous dimensions of the
lowest twist operators is formulated in terms of the Riemann surfacesComment: 37 pages, 3 figure
Non-local charges on AdS_5 x S^5 and PP-waves
We show the existence of an infinite set of non-local classically conserved
charges on the Green-Schwarz closed superstring in a pp-wave background. We
find that these charges agree with the Penrose limit of non-local classically
conserved charges recently found for the Green-Schwarz
superstring. The charges constructed in this paper could help to understand the
role played by these on the full background.Comment: 20 pages. JHEP. v2:references adde