arXiv subjects

J. Luis Miramontes

Publications and source records attributed to J. Luis Miramontes.

At least 19 recordsLinked to original sources

arXiv2025

Integrability of the $λ$-deformation of the PCM with spectators

We construct a generalisation of the $λ$-deformation of the Principal Chiral Model (PCM) where we deform just a subgroup $F$ of the full symmetry group $G$. We find that demanding Lax integrability imposes a crucial restriction, namely that the coset $F\backslash G$ must be symmetric. Surprisingly, we also find that (when $F$ is non-abelian) integrability requires that the term in the action involving only the spectator fields should have a specific $λ$-dependence, which is a curious modification of the procedure expected from the known $F=G$ case. The resulting Lax connection has a novel analytical structure, with four single poles as opposed to the two poles of the cases of the PCM and of the standard $λ$-deformation. We also explicitly work out the example of $G=SU(2)$ and $F=U(1)$, discussing its renormalisation group flow to two loops.

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arXiv2022

Homogeneous Yang-Baxter deformations as undeformed yet twisted models

The homogeneous Yang-Baxter deformation is part of a larger web of integrable deformations and dualities that recently have been studied with motivations in integrable $σ$-models, solution-generating techniques in supergravity and Double Field Theory, and possible generalisations of the AdS/CFT correspondence. The $σ$-models obtained by the homogeneous Yang-Baxter deformation with periodic boundary conditions on the worldsheet are on-shell equivalent to undeformed models, yet with twisted boundary conditions. While this has been known for some time, the expression provided so far for the twist features non-localities (in terms of the degrees of freedom of the deformed model) that prevent practical calculations, and in particular the construction of the classical spectral curve. We solve this problem by rewriting the equation defining the twist in terms of the degrees of freedom of the undeformed yet twisted model, and we show that we are able to solve it in full generality. Remarkably, this solution is a local expression. We discuss the consequences of the twist at the level of the monodromy matrix and of the classical spectral curve, analysing in particular the concrete examples of abelian, almost abelian and Jordanian deformations of the Yang-Baxter class.

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arXiv2020

Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring

The classical spectral curve for the worldsheet theory of the AdS_5 x S^5 lambda superstring is constructed. The lambda string is interpreted as a regularized, non-abelian T dual of the AdS_5 x S^5 superstring with respect to full PSU(2,2|4) symmetry. The form of the curve is identified as the semi-classical limit of a set of Bethe ansatz equations for an XXZ type spin chain for the supergroup PSU(2,2|4) in contrast to the string in AdS_5 x S^5 which is XXX type.

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arXiv2017

Giant Magnons of String Theory in the Lambda Background

The analogues of giant magnon configurations are studied on the string world sheet in the lambda background. This is a discrete deformation of the AdS(5)xS(5) background that preserves the integrability of the world sheet theory. Giant magnon solutions are generated using the dressing method and their dispersion relation is found. This reduces to the usual dyonic giant magnon dispersion relation in the appropriate limit and becomes relativistic in another limit where the lambda model becomes the generalized sine-Gordon theory of the Pohlmeyer reduction. The scattering of giant magnons is then shown in the semi-classical limit to be described by the quantum S-matrix that is a quantum group deformation of the conventional giant magnon S-matrix. It is further shown that in the small g limit, a sector of the S-matrix is related to the XXZ spin chain whose spectrum matches the spectrum of magnon bound states.

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arXiv2015

S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models

Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the k deformations associated to the more general q deformations but with q=exp(i pi/k) a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.

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arXiv2014

An Integrable Deformation of the AdS5 x S5 Superstring

The S-matrix on the world-sheet theory of the string in AdS5 x S5 has previously been shown to admit a deformation where the symmetry algebra is replaced by the associated quantum group. The case where q is real has been identified as a particular deformation of the Green-Schwarz sigma model. An interpretation of the case with q a root of unity has, until now, been lacking. We show that the Green-Schwarz sigma model admits a discrete deformation which can be viewed as a rather simple deformation of the F/F_V gauged WZW model, where F=PSU(2,2|4). The deformation parameter q is then a k-th root of unity where k is the level. The deformed theory has the same equations-of-motion as the Green-Schwarz sigma model but has a different symplectic structure. We show that the resulting theory is integrable and has just the right amount of kappa-symmetries that appear as a remnant of the fermionic part of the original gauge symmetry. This points to the existence of a fully consistent deformed string background.

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arXiv2014

Integrable Deformations of Strings on Symmetric Spaces

A general class of deformations of integrable sigma-models with symmetric space F/G target-spaces are found. These deformations involve defining the non-abelian T dual of the sigma-model and then replacing the coupling of the Lagrange multiplier imposing flatness with a gauged F/F WZW model. The original sigma-model is obtained in the limit of large level. The resulting deformed theories are shown to preserve both integrability and the equations-of-motion, but involve a deformation of the symplectic structure. It is shown that this deformed symplectic structure involves a linear combination of the original Poisson bracket and a generalization of the Faddeev-Reshetikhin Poisson bracket which we show can be re-expressed as two decoupled F current algebras. It is then shown that the deformation can be incorporated into the classical model of strings on R x F/G via a generalization of the Pohlmeyer reduction. In this case, in the limit of large sigma-model coupling it is shown that the theory becomes the relativistic symmetric space sine-Gordon theory. These results point to the existence of a deformation of this kind for the full Green-Schwarz superstring on AdS5 x S5.

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arXiv2014

Symplectic Deformations of Integrable Field Theories and AdS/CFT

Relativistic integrable field theories like the sine-Gordon equation have an infinite set of conserved charges. In a light-front formalism these conserved charges are closely related to the integrable modified KdV hierarchy at the classical level. The latter hierarchy admits a family of symplectic structures which we argue can be viewed as deformations of the relativistic sine-Gordon symplectic structure. These deformed theories are integrable but no longer relativistic and the basic excitations of the theory, the solitons, have an interesting non-relativistic dispersion relation that in a certain limit becomes the dispersion relation of dyonic giant magnons of string theory in the AdS/CFT correspondence. We argue that the deformed classical theories can be lifted to quantum theories when the sine-Gordon theory is embedded in a larger theory that describes the string world-sheet sigma model in AdS(5)xS(5).

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arXiv2013

Restoring Unitarity in the q-Deformed World-Sheet S-Matrix

The world-sheet S-matrix of the string in AdS5 x S5 has been shown to admit a q-deformation that relates it to the S-matrix of a generalization of the sine-Gordon theory, which arises as the Pohlmeyer reduction of the superstring. Whilst this is a fascinating development the resulting S-matrix is not explicitly unitary. The problem has been known for a long time in the context of S-matrices related to quantum groups. A braiding relation often called "unitarity" actually only corresponds to quantum field theory unitarity when the S-matrix is Hermitian analytic and quantum group S-matrices manifestly violate this. On the other hand, overall consistency of the S-matrix under the bootstrap requires that the deformation parameter is a root of unity and consequently one is forced to perform the "vertex" to IRF, or SOS, transformation on the states to truncate the spectrum consistently. In the IRF formulation unitarity is now manifest and the string S-matrix and the S-matrix of the generalised sine-Gordon theory are recovered in two different limits. In the latter case, expanding the Yang-Baxter equation we find that the tree-level S-matrix of the Pohlmeyer-reduced string should satisfy a modified classical Yang-Baxter equation explaining the apparent anomaly in the perturbative computation. We show that the IRF form of the S-matrix meshes perfectly with the bootstrap equations.

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arXiv2013

The Structure of Non-Abelian Kinks

We consider a class of integrable quantum field theories in 1+1 dimensions whose classical equations have kink solutions with internal collective coordinates that transform under a non-abelian symmetry group. These generalised sine-Gordon theories have been shown to be related to the world sheet theory of the string in the AdS/CFT correspondence. We provide a careful analysis of the boundary conditions at spatial infinity complicated by the fact that they are defined by actions with a WZ term. We go on to describe the local and non-local charges carried by the kinks and end by showing that their structure is perfectly consistent with the exact factorizable S-matrices that have been proposed to describe these theories.

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arXiv2012

Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix

The investigation of the q deformation of the S-matrix for excitations on the string world sheet in AdS5 x S5 is continued. We argue that due to the lack of Lorentz invariance the situation is more subtle than in a relativistic theory in that the nature of bound states depends on their momentum. At low enough momentum |p| 1. This subtlety fixes a problem involving the consistency of crossing symmetry with the relativistic limit found in earlier work. With mirror kinematics, obtained after a double Wick rotation, the bound state structure is simpler and there are no marginally unstable bound states.

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arXiv2011

q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit

A set of four factorizable non-relativistic S-matrices for a multiplet of fundamental particles are defined based on the R-matrix of the quantum group deformation of the centrally extended superalgebra su(2|2). The S-matrices are a function of two independent couplings g and q=exp(iπ/k). The main result is to find the scalar factor, or dressing phase, which ensures that the unitarity and crossing equations are satisfied. For generic (g,k), the S-matrices are branched functions on a product of rapidity tori. In the limit k->infinity, one of them is identified with the S-matrix describing the magnon excitations on the string world sheet in AdS5 x S5, while another is the mirror S-matrix that is needed for the TBA. In the g->infinity limit, the rapidity torus degenerates, the branch points disappear and the S-matrices become meromorphic functions, as required by relativistic S-matrix theory. However, it is only the mirror S-matrix which satisfies the correct relativistic crossing equation. The mirror S-matrix in the relativistic limit is then closely related to that of the semi-symmetric space sine-Gordon theory obtained from the string theory by the Pohlmeyer reduction, but has anti-symmetric rather than symmetric bound states. The interpolating S-matrix realizes at the quantum level the fact that at the classical level the two theories correspond to different limits of a one-parameter family of symplectic structures of the same integrable system.

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arXiv2011

A Relativistic Relative of the Magnon S-Matrix

We construct a relativistic scattering theory based on a q deformation and large string tension limit of the magnon S-matrix of the string world sheet theory in AdS_5 x S^5. The S-matrix falls naturally into a previously studied class associated to affine quantum groups, in this case for a twisted affine loop superalgebra associated to an outer automorphism of sl(2|2). This infinite algebra includes the celebrated triply extended psl(2|2) x R^3 algebra, but only two of the centres, the lightcone components of the 2-momentum, are non-vanishing. The algebra has the interpretation as an extended supersymmetry algebra including a non-trivial R-symmetry. The representation theory of this algebra has some complications in that tensor products are reducible but indecomposable, however, we find that structure meshes perfectly with the bootstrap, or fusion, equations of S-matrix theory. The bootstrap equations can then be used inductively to generate the complete S-matrix. Unlike the magnon theory, the relativistic theory only has a finite set of states and we find that - at least when the deformation parameter q is a root of unity - the spectrum matches precisely the soliton spectrum of the relativistic theory underlying the Pohlmeyer reduction of the string world sheet theory known as the semi-symmetric space sine-Gordon theory.

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arXiv2011

The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory

The generalized symmetric space sine-Gordon theories are a series of 1+1-integrable field theories that are classically equivalent to superstrings on symmetric space spacetimes F/G. They are formulated in terms of a semi-symmetric space as a gauged WZW model with fermions and a potential term to deform it away from the conformal fixed point. We consider in particular the case of PSU(2,2|4)/Sp(2,2)xSp(4) which corresponds to AdS(5)xS(5). We argue that the infinite tower of conserved charges of these theories includes an exotic N=(8,8) supersymmetry that is realized in a mildy non-local way at the Lagrangian level. The supersymmetry is associated to a double central extension of the superalgebra psu(2|2)+psu(2|2) and includes a non-trivial R symmetry algebra corresponding to global gauge transformations, as well as 2-dimensional spacetime translations. We then explicitly construct soliton solutions and show that they carry an internal moduli superspace CP(2|1)xCP(2|1) with both bosonic and Grassmann collective coordinates. We show how to semi-classical quantize the solitons by writing an effective quantum mechanical system on the moduli space which takes the form of a co-adjoint orbit of SU(2|2)xSU(2|2). The spectrum consists of a tower of massive states in the short, or atypical, symmetric representations, just as the giant magnon states of the string world sheet theory, although here the tower is truncated.

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arXiv2011

The Semi-Classical Spectrum of Solitons and Giant Magnons

In this note, we summarize recent progress in constructing and then semi-classically quantizing solitons, or non-abelian Q-balls, in the symmetric space sine-Gordon theories. We then consider the images of these solitons in the related constrained sigma model, which are the dyonic giant magnons on the string theory world-sheet. Focussing on the case of the symmetric space S^5, we perform a semi-classical quantization of the solitons and magnons and show that both lead to Chern-Simons quantum mechanics on the internal moduli space which is a real Grassmannian SO(4)/SO(2)xSO(2) but---importantly---with a different coupling constant. Quantizing this system shows that both the Q-balls and magnons come in a tower of states transforming in symmetric representations of the SO(4) symmetry group; however, the former come in a finite tower whereas the latter come in the well-known infinite tower of dyonic giant magnons.

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arXiv2011

Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories

We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1+1-dimensions which are associated to a symmetric space F/G, and are related via the Pohlmeyer reduction to theories of strings moving on symmetric spaces. We show that the solitons are kinks that carry an internal moduli space that can be identified with a particular co-adjoint orbit of the unbroken subgroup H of G. Classically the solitons come in a continuous spectrum which encompasses the perturbative fluctuations of the theory as the kink charge becomes small. We show that the solitons can be quantized by allowing the collective coordinates to be time-dependent to yield a form of quantum mechanics on the co-adjoint orbit. The quantum states correspond to symmetric tensor representations of the symmetry group H and have the interpretation of a fuzzy geometric version of the co-adjoint orbit. The quantized finite tower of soliton states includes the perturbative modes at the base.

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arXiv2010

The Relativistic Avatars of Giant Magnons and their S-Matrix

The motion of strings on symmetric space target spaces underlies the integrability of the AdS/CFT correspondence. Although these theories, whose excitations are giant magnons, are non-relativistic they are classically equivalent, via the Polhmeyer reduction, to a relativistic integrable field theory known as a symmetric space sine-Gordon theory. These theories can be formulated as integrable deformations of gauged WZW models. In this work we consider the class of symmetric spaces CP^{n+1} and solve the corresponding generalized sine-Gordon theories at the quantum level by finding the exact spectrum of topological solitons, or kinks, and their S-matrix. The latter involves a trignometric solution of the Yang-Baxer equation which exhibits a quantum group symmetry with a tower of states that is bounded, unlike for magnons, as a result of the quantum group deformation parameter q being a root of unity. We test the S-matrix by taking the semi-classical limit and comparing with the time delays for the scattering of classical solitons. We argue that the internal CP^{n-1} moduli space of collective coordinates of the solitons in the classical theory can be interpreted as a q-deformed fuzzy space in the quantum theory. We analyse the n=1 case separately and provide a further test of the S-matrix conjecture in this case by calculating the central charge of the UV CFT using the thermodynamic Bethe Ansatz.

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arXiv2009

A New and Elementary CP^n Dyonic Magnon

We show that the dressing transformation method produces a new type of dyonic CP^n magnon in terms of which all the other known solutions are either composites or arise as special limits. In particular, this includes the embedding of Dorey's dyonic magnon via an RP^3 subspace of CP^n. We also show how to generate Dorey's dyonic magnon directly in the S^n sigma model via the dressing method without resorting to the isomorphism with the SU(2) principle chiral model when n=3. The new dyon is shown to be either a charged dyon or topological kink of the related symmetric-space sine-Gordon theories associated to CP^n and in this sense is a direct generalization of the soliton of the complex sine-Gordon theory.

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