1,900 research outputs found
Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups
Quantum planes which correspond to all one parameter solutions of QYBE for
the two-dimensional case of GL-groups are summarized and their geometrical
interpretations are given. It is shown that the quantum dual plane is
associated with an exotic solution of QYBE and the well-known quantum -plane
may be regarded as the quantum analog of the flag (or fiber) plane.
Contractions of the quantum supergroup and corresponding quantum
superspace are considered in Cartesian basis. The contracted
quantum superspace is interpreted as the non-commutative
analog of the superspace with the fiber odd part.Comment: Talk given at the XIII Int. Coll. on Integrable Systems and Quantum
Groups, June 17-19, 2004, Prague, Czech Republic. Submitted in Czech. J. of
Physic
On contractions of classical basic superalgebras
We define a class of orthosymplectic and unitary
superalgebras which may be obtained from and
by contractions and analytic continuations in a similar way as the
special linear, orthogonal and the symplectic Cayley-Klein algebras are
obtained from the corresponding classical ones. Casimir operators of
Cayley-Klein superalgebras are obtained from the corresponding operators of the
basic superalgebras. Contractions of and are regarded as
an examples.Comment: 15 pages, Late
Analytic Solution of Bremsstrahlung TBA
We consider the quark--anti-quark potential on the three sphere or the
generalized cusp anomalous dimension in planar N=4 SYM. We concentrate on the
vacuum potential in the near BPS limit with units of R-charge.
Equivalently, we study the anomalous dimension of a super-Wilson loop with L
local fields inserted at a cusp. The system is described by a recently proposed
infinite set of non-linear integral equations of the Thermodynamic Bethe Ansatz
(TBA) type. That system of TBA equations is very similar to the one of the
spectral problem but simplifies a bit in the near BPS limit. Using techniques
based on the Y-system of functional equations we first reduced the infinite
system of TBA equations to a Finite set of Nonlinear Integral Equations
(FiNLIE). Then we solve the FiNLIE system analytically, obtaining a simple
analytic result for the potential! Surprisingly, we find that the system has
equivalent descriptions in terms of an effective Baxter equation and in terms
of a matrix model. At L=0, our result matches the one obtained before using
localization techniques. At all other L's, the result is new. Having a new
parameter, L, allows us to take the large L classical limit. We use the matrix
model description to solve the classical limit and match the result with a
string theory computation. Moreover, we find that the classical string
algebraic curve matches the algebraic curve arising from the matrix model.Comment: 50 pages, 5 figures. v2: references added, JHEP versio
Six and seven loop Konishi from Luscher corrections
In the present paper we derive six and seven loop formulas for the anomalous
dimension of the Konishi operator in N=4 SYM from string theory using the
technique of Luscher corrections. We derive analytically the integrand using
the worldsheet S-matrix and evaluate the resulting integral and infinite sum
using a combination of high precision numerical integration and asymptotic
expansion. We use this high precision numerical result to fit the integer
coefficients of zeta values in the final analytical answer. The presented six
and seven loop results can be used as a cross-check with FiNLIE on the string
theory side, or with direct gauge theory computations. The seven loop level is
the theoretical limit of this Luscher approach as at eight loops
double-wrapping corrections will appear.Comment: 18 pages, typos correcte
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
Quantum folded string and integrability: from finite size effects to Konishi dimension
Using the algebraic curve approach we one-loop quantize the folded string
solution for the type IIB superstring in AdS(5)xS(5). We obtain an explicit
result valid for arbitrary values of its Lorentz spin S and R-charge J in terms
of integrals of elliptic functions. Then we consider the limit S ~ J ~ 1 and
derive the leading three coefficients of strong coupling expansion of short
operators. Notably, our result evaluated for the anomalous dimension of the
Konishi state gives 2\lambda^{1/4}-4+2/\lambda^{1/4}. This reproduces correctly
the values predicted numerically in arXiv:0906.4240. Furthermore we compare our
result using some new numerical data from the Y-system for another similar
state. We also revisited some of the large S computations using our methods. In
particular, we derive finite--size corrections to the anomalous dimension of
operators with small J in this limit.Comment: 20 pages, 1 figure; v2: references added, typos corrected; v3: major
improvement of the references; v4: Discussion of short operators is
restricted to the case n=1. This restriction does not affect the main results
of the pape
First-principles derivation of the AdS/CFT Y-systems
We provide a first-principles, perturbative derivation of the AdS5/CFT4
Y-system that has been proposed to solve the spectrum problem of N=4 SYM. The
proof relies on the computation of quantum effects in the fusion of some loop
operators, namely the transfer matrices. More precisely we show that the
leading quantum corrections in the fusion of transfer matrices induce the
correct shifts of the spectral parameter in the T-system. As intermediate steps
we study UV divergences in line operators up to first order and compute the
fusion of line operators up to second order for the pure spinor string in
AdS5xS5. We also argue that the derivation can be easily extended to other
integrable models, some of which describe string theory on AdS4, AdS3 and AdS2
spacetimes.Comment: 45 pages, 5 figures; v2: minor additions, JHEP versio
Exact computation of one-loop correction to energy of pulsating strings in AdS_5 x S^5
In the present paper, which is a sequel to arXiv:1001:4018, we compute the
one-loop correction to the energy of pulsating string solutions in AdS_5 x S^5.
We show that, as for rigid spinning string elliptic solutions, the fluctuation
operators for pulsating solutions can be also put into the single-gap Lame'
form. A novel aspect of pulsating solutions is that the one-loop correction to
their energy is expressed in terms of the stability angles of the quadratic
fluctuation operators. We explicitly study the "short string" limit of the
corresponding one-loop energies, demonstrating a certain universality of the
form of the energy of "small" semiclassical strings. Our results may help to
shed light on the structure of strong-coupling expansion of anomalous
dimensions of dual gauge theory operators.Comment: 49 pages; v2: appendix F and note about antiperiodic fermions added,
typos corrected, references adde
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