95 research outputs found
Quantum Sine(h)-Gordon Model and Classical Integrable Equations
We study a family of classical solutions of modified sinh-Gordon equation,
$\partial_z\partial_{{\bar z}} \eta-\re^{2\eta}+p(z)\,p({\bar z})\
\re^{-2\eta}=0p(z)=z^{2\alpha}-s^{2\alpha}Q(\alpha>0)(\alpha<-1)$ models.Comment: 35 pages, 3 figure
On the Use of Quantum Algebras in Rotation-Vibration Spectroscopy
A two-parameter deformation of the Lie algebra u is used, in conjunction
with the rotor system and the oscillator system, to generate a model for
rotation-vibration spectroscopy of molecules and nuclei.Comment: 10 pages, Latex File, published in Modern Group Theoretical Methods
in Physics, J. Bertrand et al. (eds.), Kluwer Academic Publishers (1995),
27-3
From Koszul duality to Poincar\'e duality
We discuss the notion of Poincar\'e duality for graded algebras and its
connections with the Koszul duality for quadratic Koszul algebras. The
relevance of the Poincar\'e duality is pointed out for the existence of twisted
potentials associated to Koszul algebras as well as for the extraction of a
good generalization of Lie algebras among the quadratic-linear algebras.Comment: Dedicated to Raymond Stora. 27 page
Quantum integrability of the Alday-Arutyunov-Frolov model
We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF)
model by calculating the three-particle scattering amplitude at the first
non-trivial order and showing that the S-matrix is factorizable at this order.
We consider a more general fermionic model and find a necessary constraint to
ensure its integrability at quantum level. We then show that the quantum
integrability of the AAF model follows from this constraint. In the process, we
also correct some missed points in earlier works.Comment: 40 pages; Replaced with published version. Appendix and comments
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Twisted Yangians for symmetric pairs of types B, C, D
We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan's classification. These algebras can be regarded as coideal subalgebras of the extended Yangian for orthogonal or symplectic Lie algebras. They can also be presented as quotients of a reflection algebra by additional symmetry relations. We prove an analogue of the Poincare-Birkoff-Witt Theorem, determine their centres and study also extended reflection algebras
Twisted Bethe equations from a twisted S-matrix
All-loop asymptotic Bethe equations for a 3-parameter deformation of
AdS5/CFT4 have been proposed by Beisert and Roiban. We propose a Drinfeld twist
of the AdS5/CFT4 S-matrix, together with c-number diagonal twists of the
boundary conditions, from which we derive these Bethe equations. Although the
undeformed S-matrix factorizes into a product of two su(2|2) factors, the
deformed S-matrix cannot be so factored. Diagonalization of the corresponding
transfer matrix requires a generalization of the conventional algebraic Bethe
ansatz approach, which we first illustrate for the simpler case of the twisted
su(2) principal chiral model. We also demonstrate that the same twisted Bethe
equations can alternatively be derived using instead untwisted S-matrices and
boundary conditions with operatorial twists.Comment: 42 pages; v2: a new appendix on sl(2) grading, 2 additional
references, and some minor changes; v3: improved Appendix D, additional
references, and further minor changes, to appear in JHE
Integrability of Green-Schwarz Sigma Models with Boundaries
We construct integrability preserving boundary conditions for Green-Schwarz
sigma-models on semi-symmetric spaces. The boundary conditions are expressed as
gluing conditions of the flat-connection, using an involutive metric preserving
automorphism. We show that the boundary conditions preserve half of the
space-time supersymmetry and an infinite set of conserved charges. We find
integrable D-brane configurations for AdS_5 x S^5 and AdS_4 x CP^3 backgrounds.Comment: 24 pages. v2 references added. v3 typos fixed, sec. 3 improved,
references added, published versio
Wave functions and correlation functions for GKP strings from integrability
We develop a general method of computing the contribution of the vertex
operators to the semi-classical correlation functions of heavy string states,
based on the state-operator correspondence and the integrable structure of the
system. Our method requires only the knowledge of the local behavior of the
saddle point configuration around each vertex insertion point and can be
applied to cases where the precise forms of the vertex operators are not known.
As an important application, we compute the contributions of the vertex
operators to the three-point functions of the large spin limit of the
Gubser-Klebanov-Polyakov (GKP) strings in spacetime, left unevaluated
in our previous work [arXiv:1110.3949] which initiated such a study. Combining
with the finite part of the action already computed previously and with the
newly evaluated divergent part of the action, we obtain finite three-point
functions with the expected dependence of the target space boundary coordinates
on the dilatation charge and the spin.Comment: 80 pages, 7 figures, v2: typos and minor errors corrected, a
reference added, v3: typos and a reference corrected, published versio
Classical Conformal Blocks and Accessory Parameters from Isomonodromic Deformations
Classical conformal blocks naturally appear in the large central charge limit
of 2D Virasoro conformal blocks. In the correspondence, they
are related to classical bulk actions and are used to calculate entanglement
entropy and geodesic lengths. In this work, we discuss the identification of
classical conformal blocks and the Painlev\'e VI action showing how
isomonodromic deformations naturally appear in this context. We recover the
accessory parameter expansion of Heun's equation from the isomonodromic
-function. We also discuss how the expansion of the
-function leads to a novel approach to calculate the 4-point classical
conformal block.Comment: 32+10 pages, 2 figures; v3: upgraded notation, discussion on moduli
space and monodromies, numerical and analytic checks; v2: added refs, fixed
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Nested Algebraic Bethe Ansatz for Open Spin Chains with Even Twisted Yangian Symmetry
We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible so2n- or sp2n-representations and the monodromy matrix satisfies the defining relations of the Olshanskii twisted Yangian Y±(gl2n). We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a so2n- or sp2n-symmetric open spin chain to that of a gln-symmetric periodic spin chain. We explicitly derive the structure of the Bethe vectors and the nested Bethe equations
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