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  • 1
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    Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix Formalism (2011)
    Springer
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    Publication Date: 2011-10-02
    Description:    The one-dimensional Heisenberg XXX spin chain appears in a special limit of the AdS/CFT integrable system. We review various ways of proving its integrability, and discuss the associated methods of solution. In particular, we outline the coordinate and the algebraic Bethe ansatz, giving reference to literature suitable for learning these techniques. Finally, we speculate which of the methods might lift to the exact solution of the AdS/CFT system, and sketch a promising method for constructing the Baxter Q-operator of the XXX chain. It allows to find the spectrum of the model using certain algebraic techniques, while entirely avoiding Bethe’s ansatz. Content Type Journal Article Pages 1-18 DOI 10.1007/s11005-011-0530-9 Authors Matthias Staudacher, Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, Johann von Neumann-Haus, Rudower Chaussee 25, 12489 Berlin, Germany Journal Letters in Mathematical Physics Online ISSN 1573-0530 Print ISSN 0377-9017
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  • 2
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    Norm of Logarithmic Primary of Virasoro Algebra (2011)
    Springer
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    Publication Date: 2011-06-27
    Description:    We give an algebraic proof of the formula on the norm of logarithmic primary of Virasoro algebra, which was proposed by Al. Zamolodchikov. This formula appears in the recursion formula for the norm of Gaiotto state, which guarantees the AGT relation for the four-dimensional SU(2) pure gauge theory. Content Type Journal Article Pages 1-24 DOI 10.1007/s11005-011-0502-0 Authors Shintarou Yanagida, Department of Mathematics, Kobe University, Rokko, Kobe, 657-8501 Japan Journal Letters in Mathematical Physics Online ISSN 1573-0530 Print ISSN 0377-9017
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  • 3
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    Eigenvalue Bounds for Schrödinger Operators with a Homogeneous Magnetic Field (2011)
    Springer
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    Publication Date: 2011-06-11
    Description:    We prove Lieb-Thirring inequalities for Schrödinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength of the magnetic field, and hence quantifies the diamagnetic behavior of the system. For a harmonic oscillator in a homogenous magnetic field, we obtain the sharp constants in the inequalities. Content Type Journal Article Pages 1-15 DOI 10.1007/s11005-011-0499-4 Authors Rupert L. Frank, Department of Mathematics, Princeton University, Princeton, NJ 08544, USA Rikard Olofsson, Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden Journal Letters in Mathematical Physics Online ISSN 1573-0530 Print ISSN 0377-9017
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  • 4
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    The Dirac Sea (2011)
    Springer
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    Publication Date: 2011-05-14
    Description:    We give an alternate definition of the free Dirac field featuring an explicit construction of the Dirac sea. The treatment employs a semi-infinite wedge product of Hilbert spaces. We also show that the construction is equivalent to the standard Fock space construction. Content Type Journal Article Pages 1-10 DOI 10.1007/s11005-011-0496-7 Authors Jonathan Dimock, Department of Mathematics, SUNY at Buffalo, Buffalo, NY 14260, USA Journal Letters in Mathematical Physics Online ISSN 1573-0530 Print ISSN 0377-9017
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  • 5
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    Lipschitz-Continuity of the Integrated Density of States for Gaussian Random Potentials (2011)
    Springer
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    Publication Date: 2011-02-21
    Description:    The integrated density of states of a Schrödinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive mean, is locally uniformly Lipschitz-continuous. This is proven using a Wegner estimate. Content Type Journal Article Pages 1-3 DOI 10.1007/s11005-011-0465-1 Authors Ivan Veselić, Fakultät für Mathematik, Technische. Universität Chemnitz, 09107 TU-Chemnitz, Germany Journal Letters in Mathematical Physics Online ISSN 1573-0530 Print ISSN 0377-9017
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  • 6
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    Scaling Limits for the System of Semi-Relativistic Particles Coupled to a Scalar Bose Field (2011)
    Springer
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    Publication Date: 2011-04-01
    Description:    In this paper, the Hamiltonian for the system of semi-relativistic particles interacting with a scalar Bose field is investigated. A scaled total Hamiltonian of the system is defined and its scaling limit is considered. Then, a semi-relativistic Schrödinger operator with an effective potential is derived. Content Type Journal Article Pages 1-13 DOI 10.1007/s11005-011-0487-8 Authors Toshimitsu Takaesu, Faculty of Mathematics, Kyushu University, Fukuoka, 812-8581 Japan Journal Letters in Mathematical Physics Online ISSN 1573-0530 Print ISSN 0377-9017
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  • 7
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    Appendix: Publication List of Vladimir B. Matveev (2011)
    Springer
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    Publication Date: 2011-04-01
    Description: Appendix: Publication List of Vladimir B. Matveev Content Type Journal Article Pages 1-8 DOI 10.1007/s11005-011-0486-9 Journal Letters in Mathematical Physics Online ISSN 1573-0530 Print ISSN 0377-9017
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  • 8
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    Spectral Action for Scalar Perturbations of Dirac Operators (2011)
    Springer
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    Publication Date: 2011-10-05
    Description:    We investigate the leading terms of the spectral action for odd-dimensional Riemannian spin manifolds with the Dirac operator perturbed by a scalar function. We calculate first two Gilkey–de Witt coefficients and make explicit calculations for the case of n -spheres with a completely symmetric Dirac. In the special case of dimension 3, when such perturbation corresponds to the completely antisymmetric torsion, we carry out the noncommutative calculation following Chamseddine and Connes (J Geom Phys 57:121, 2006 ) and study the case of SU q (2). Content Type Journal Article Pages 1-16 DOI 10.1007/s11005-011-0498-5 Authors Andrzej Sitarz, Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland Artur Zając, Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland Journal Letters in Mathematical Physics Online ISSN 1573-0530 Print ISSN 0377-9017
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  • 9
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    Vortex Counting and Lagrangian 3-Manifolds (2011)
    Springer
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    Publication Date: 2011-10-09
    Description:    To every 3-manifold M one can associate a two-dimensional N =(2, 2) supersymmetric field theory by compactifying five-dimensional N =2 super-Yang–Mills theory on M . This system naturally appears in the study of half-BPS surface operators in four-dimensional N =2 gauge theories on one hand, and in the geometric approach to knot homologies, on the other. We study the relation between vortex counting in such two-dimensional N =(2, 2) supersymmetric field theories and the refined BPS invariants of the dual geometries. In certain cases, this counting can also be mapped to the computation of degenerate conformal blocks in two-dimensional CFT’s. Degenerate limits of vertex operators in CFT receive a simple interpretation via geometric transitions in BPS counting. Content Type Journal Article Pages 1-63 DOI 10.1007/s11005-011-0531-8 Authors Tudor Dimofte, California Institute of Technology, Pasadena, CA 91125, USA Sergei Gukov, California Institute of Technology, Pasadena, CA 91125, USA Lotte Hollands, California Institute of Technology, Pasadena, CA 91125, USA Journal Letters in Mathematical Physics Online ISSN 1573-0530 Print ISSN 0377-9017
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  • 10
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    Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve (2011)
    Springer
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    Publication Date: 2011-09-05
    Description:    We review the spectral curve for the classical string in AdS 5 × S 5 . Classical integrability of the AdS 5  × S 5 string implies the existence of a flat connection, whose monodromies generate an infinite set of conserved charges. The spectral curve is constructed out of the quasi-momenta, which are eigenvalues of the monodromy matrix, and each finite-gap classical solution can be characterized in terms of such a curve. This provides a concise and powerful description of the classical solution space. In addition, semi-classical quantization of the string can be performed in terms of the quasi-momenta. We review the general frame-work of the semi-classical quantization in this context and exemplify it with the circular string solution which is supported on \mathbb R × S 3 Ì AdS 5 × S 5 . Content Type Journal Article Pages 1-22 DOI 10.1007/s11005-011-0525-6 Authors Sakura Schäfer-Nameki, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, 93106 CA, USA Journal Letters in Mathematical Physics Online ISSN 1573-0530 Print ISSN 0377-9017
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