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  • 1. Bundzik, Daniel
    et al.
    Månsson, Teresia
    The General Leigh-Strassler deformation and integrability2006In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 1, no 116Article in journal (Refereed)
    Abstract [en]

    The success of the identification of the planar dilatation operator of = 4 SYM with an integrable spin chain Hamiltonian has raised the question if this also is valid for a deformed theory. Several deformations of SYM have recently been under investigation in this context. In this work we consider the general Leigh-Strassler deformation. For the generic case the S-matrix techniques cannot be used to prove integrability. Instead we use R-matrix techniques to study integrability. Some new integrable points in the parameter space are found.

  • 2. Fjelstad, Jens
    et al.
    Månsson, Teresia
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    New symmetries of the chiral Potts model2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 15, p. 155208-Article in journal (Refereed)
    Abstract [en]

    In this paper a hitherto unknown spectrum generating algebra, consisting of two coupled Temperley-Lieb algebras, is found in the three-state chiral Potts model. From this, we can construct new Onsager integrable models. One realization is in terms of a staggered isotropic XY spin chain. Further we investigate the importance of the algebra for the existence of mutually commuting conserved charges. This leads us to a natural generalization of the boost operator, which generates the charges.

  • 3. Lahtinen, V.
    et al.
    Månsson, Teresia
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Ardonne, E.
    Hierarchy of exactly solvable spin- 1 2 chains with s o (N) 1 critical points2014In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 89, no 1, p. 014409-Article in journal (Refereed)
    Abstract [en]

    We construct a hierarchy of exactly solvable spin-1/2 chains with so(N)1 critical points. Our construction is based on the framework of condensate-induced transitions between topological phases. We employ this framework to construct a Hamiltonian term that couples N transverse field Ising chains such that the resulting theory is critical and described by the so(N)1 conformal field theory. By employing spin duality transformations, we then cast these spin chains for arbitrary N into translationally invariant forms that all allow exact solution by the means of a Jordan-Wigner transformation. For odd N our models generalize the phase diagram of the transverse field Ising chain, the simplest model in our hierarchy. For even N the models can be viewed as longer ranger generalizations of the XY chain, the next model in the hierarchy. We also demonstrate that our method of constructing spin chains with given critical points goes beyond exactly solvable models. Applying the same strategy to the Blume-Capel model, a spin-1 generalization of the Ising chain in a generic magnetic field, we construct another critical spin-1 chain with the predicted conformal field theory (CFT) describing the criticality.

  • 4.
    Månsson, Teresia
    ax-Planck Institut für Gravitationsphysik.
    Is there a tower of charges to be discovered?2007In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 41, p. 194014-Article in journal (Refereed)
    Abstract [en]

    We investigate higher-loop integrability for a q-deformation of the -sector of SYM theory. First we construct a generalization of the long-range spin chain, which for the lowest orders describes the non-deformed dilatation operator. This generalized model is built up from Temperley–Lieb algebra generators and describes the deformed theory to at least two loops. When constructing the model we have demanded the existence of one commuting charge, which puts strong constraints on the parameters to three-loop orders. We also write the five first charges for this model at two-loops order. Our main goal is to obtain an explicit expression for an infinite number of commuting charges, all commuting with the dilatation operator. This would imply integrability. As a step towards this goal we present in this paper an expression for a generic local charge of the one-loop dilatation operator, which happens to be a generator of the Temperley–Lieb algebra.

  • 5.
    Månsson, Teresia
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    The Liegh-Strassler deformation and the quest for integrability2007In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479Article in journal (Refereed)
    Abstract [en]

    In this paper we study the one-loop dilatation operator of the full scalar field sector of Leigh-Strassler deformed =4 SYM theory. In particular we map it onto a spin chain and find the parameter values for which the Reshetikhin integrability criteria are fulfilled. Some years ago Roiban found an integrable subsector, consisting of two holomorphic scalar fields, corresponding to the XXZ model. He was pondering about the existence of a subsector which would form generalisation of that model to an integrable q(3) model. Later Berenstein and Cherkis added one more holomorphic field and showed that the subsector obtained this way cannot be integrable except for the case when q = eiβ, β. In this work we show if we add an anti-holomorphic field to the two holomorphic ones, we get indeed an integrable q(3) subsector. We find it plausible that a direct generalisation to a q(2|3) one-loop sector will exist, and possibly beyond one-loop.

  • 6.
    Månsson, Teresia
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Lahtinen, Ville
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Suorsa, Juha
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Ardonne, Eddy
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Condensate-induced transitions and critical spin chains2013In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 88, no 4, p. 041403-Article in journal (Refereed)
    Abstract [en]

    We show that condensate-induced transitions between two-dimensional topological phases provide a general framework to relate one-dimensional spin models at their critical points. We demonstrate this using two examples. First, we show that two well-known spin chains, namely, the XY chain and the transverse field Ising chain with only next-nearest-neighbor interactions, differ at their critical points only by a nonlocal boundary term and can be related via an exact mapping. The boundary term constrains the set of possible boundary conditions of the transverse field Ising chain, reducing the number of primary fields in the conformal field theory that describes its critical behavior. We argue that the reduction of the field content is equivalent to the confinement of a set of primary fields, in precise analogy to the confinement of quasiparticles resulting from a condensation of a boson in a topological phase. As the second example we show that when a similar confining boundary term is applied to the XY chain with only next-nearest-neighbor interactions, the resulting system can be mapped to a local spin chain with the u(1)(2) x u(1)(2) critical behavior predicted by the condensation framework.

  • 7.
    Månsson, Teresia
    et al.
    Albert Einstein Inst, Max Planck Inst Gravitat Phys.
    Zoubos, Konstantinos
    Univ Copenhagen, Niels Bohr Inst.
    Quantum symmetries and marginal deformations2010In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 10, p. 043-Article in journal (Refereed)
    Abstract [en]

    We study the symmetries of the N = 1 exactly marginal deformations of N = 4 Super Yang-Mills theory. For generic values of the parameters, these deformations are known to break the SU(3) part of the R-symmetry group down to a discrete subgroup. However, a closer look from the perspective of quantum groups reveals that the Lagrangian is in fact invariant under a certain Hopf algebra which is a non-standard quantum deformation of the algebra of functions on SU(3). Our discussion is motivated by the desire to better understand why these theories have significant differences from N = 4 SYM regarding the planar integrability (or rather lack thereof) of the spin chains encoding their spectrum. However, our construction works at the level of the classical Lagrangian, without relying on the language of spin chains. Our approach might eventually provide a better understanding of the finiteness properties of these theories as well as help in the construction of their AdS/CFT duals.

  • 8. Puletti, Valentina Giangreco M.
    et al.
    Månsson, Teresia
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    The dual string sigma-model of the SUq(3) sector2012In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 2012, no 1, p. 1-24Article in journal (Refereed)
    Abstract [en]

    In four-dimensional N = 4 super Yang-Mills (SYM) the SU(3) sub-sector spanned by purely holomorphic fields is isomorphic to the corresponding mixed one spanned by both holomorphic and anti-holomorphic fields. This is no longer the case when one considers the marginally deformed N = 4 SYM. The mixed SU(3) sector marginally deformed by a complex parameter beta, i.e. SUq(3) with q = e(2i pi beta), has been shown to be integrable at one-loop [1], while it is not the case for the corresponding purely holomorphic one. Moreover, the marginally deformed N = 4 SYM also has a gravity dual constructed by Lunin and Maldacena in [2]. However, the mixed SUq(3) sector has not been studied from the supergravity point of view. Hence in this note, for the case of purely imaginary marginal beta-deformations, we compute the superstring SUq (3) sigma-model in the fast spinning string limit and show that, for rational spinning strings, it reproduces the energy computed via Bethe equations.

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