53 research outputs found
A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon model
We consider the infrared (IR) limit of the nonlinear integral equations
(NLIEs) for the boundary supersymmetric sine-Gordon (BSSG) model, previously
obtained from the NLIEs for the inhomogeneous open spin-1 XXZ quantum spin
chain with general integrable boundary terms, for values of the boundary
parameters which satisfy a certain constraint. In particular, we compute the
boundary S matrix and determine the "lattice - IR" relation for the BSSG
parameters.Comment: 18 page
Revisiting the Y=0 open spin chain at one loop
In 2005, Berenstein and Vazquez determined an open spin chain Hamiltonian
describing the one-loop anomalous dimensions of determinant-like operators
corresponding to open strings attached to Y=0 maximal giant gravitons. We
construct the transfer matrix (generating functional of conserved quantities)
containing this Hamiltonian, thereby directly proving its integrability. We
find the eigenvalues of this transfer matrix and the corresponding Bethe
equations, which we compare with proposed all-loop Bethe equations. We note
that the Bethe ansatz solution has a certain "gauge" freedom, and is not
completely unique.Comment: 16 page
Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms
With the help of the F-basis provided by the Drinfeld twist or factorizing
F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we
obtain the determinant representations of the scalar products of Bethe states
of the model.Comment: Latex file, 28 pages, based on the talk given by W. -L. Yang at
Statphys 24, Cairns, Australia, 19-23 July, 201
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
Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
By dimensionally reducing the higher derivative corrections of
ten-dimensional IIB theory on a torus we deduce constraints on the E_{n+1}
automorphic forms that occur in d=10-n dimensions. In particular we argue that
these automorphic forms involve the representation of E_{n+1} with fundamental
weight \lambda^{n+1}, which is also the representation to which the string
charges in d dimensions belong. We also consider a similar calculation for the
reduction of higher derivative terms in eleven-dimensional M-theory.Comment: Minor corrections, to appear in JHE
Moduli space coordinates and excited state g-functions
We consider the space of boundary conditions of Virasoro minimal models
formed from the composition of a collection of flows generated by \phi_{1,3}.
These have recently been shown to fall naturally into a sequence, each term
having a coordinate on it in terms of a boundary parameter, but no global
parameter has been proposed. Here we investigate the idea that the overlaps of
particular bulk states with the boundary states give natural coordinates on the
moduli space of boundary conditions. We find formulae for these overlaps using
the known thermodynamic Bethe Ansatz descriptions of the ground and first
excited state on the cylinder and show that they give a global coordinate on
the space of boundary conditions, showing it is smooth and compact as expected.Comment: 10 pages, 4 figure
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