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Luis J Miramontes - One of the best experts on this subject based on the ideXlab platform.
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the ads5 s5 semi Symmetric Space sine gordon theory
Journal of High Energy Physics, 2011Co-Authors: Timothy J Hollowood, Luis J MiramontesAbstract: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) × Sp(4) which corresponds to AdS5 × S5. We argue that the infinite tower of conserved charges of these theories includes an exotic $ \mathcal{N} = \left( {8,8} \right) $ 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 $ \mathfrak{p}\mathfrak{s}\mathfrak{u}\left( {2\left| 2 \right.} \right) \oplus \mathfrak{p}\mathfrak{s}\mathfrak{u}\left( {2\left| 2 \right.} \right) $ 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 $ \mathbb{C}{P^{2\left| 1 \right.}} \times \mathbb{C}{P^{2\left| 1 \right.}} $ 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)×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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the Symmetric Space and homogeneous sine gordon theories
Nuclear Physics, 1997Co-Authors: Carlos R Fernandezpousa, M V Gallas, J Hollowood, Luis J MiramontesAbstract:Two series of integrable theories are constructed which have soliton solutions and can be thought of as generalizations of the sine-Gordon theory. They exhibit internal symmetries and can be described as gauged WZW theories with a potential term. The spectrum of massive states is determined.
Matthew B Stenzel - One of the best experts on this subject based on the ideXlab platform.
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an inversion formula for the segal bargmann transform on a Symmetric Space of non compact type
Journal of Functional Analysis, 2006Co-Authors: Matthew B StenzelAbstract:Abstract We prove analogs of the heat kernel transform inversion formulae of Golse, Leichtnam and the author [E. Leichtnam, F. Golse, M. Stenzel, Intrinsic microlocal analysis and inversion formulae for the heat equation on compact real-analytic Riemannian manifolds, Ann. Sci. Ecole Norm. Sup. (4) 29 (6) (1996) 669–736. MR1422988 (97h:58153), Theorems 0.3, 0.4] in the setting of a Riemannian Symmetric Space of Helgason's non-compact type.
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the segal bargmann transform on a Symmetric Space of compact type
Journal of Functional Analysis, 1999Co-Authors: Matthew B StenzelAbstract:Abstract We study the Segal–Bargmann transform on a Symmetric Space X of compact type, mapping L 2 ( X ) into holomorphic functions on the complexification X C . We invert this transform by integrating against a “dual” heat kernel measure in the fibers of a natural fibration of X C over X . We prove that the Segal–Bargmann transform is an isometry from L 2 ( X ) onto the Space of holomorphic functions on X C which are square integrable with respect to a natural measure. These results extend those of B. Hall in the compact group case.
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ricci flat metrics on the complexification of a compact rank one Symmetric Space
Manuscripta Mathematica, 1993Co-Authors: Matthew B StenzelAbstract:We construct a complete Ricci-flat Kahler metric on the complexification of a compact rank one Symmetric Space. Our method is to look for a Kahler potential of the form ψ = ƒ(u), whereu satisfies the homogeneous Monge-Ampere equation. We use the high degree of symmetry present to reduce the non-linear partial differential equation governing the Ricci curvature to a simple second-order ordinary differential equation for the functionf. To prove that the resulting metric is complete requires some techniques from symplectic geometry.
Rudra P Sarkar - One of the best experts on this subject based on the ideXlab platform.
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on the schwartz Space isomorphism theorem for rank one Symmetric Space
arXiv: Representation Theory, 2007Co-Authors: Joydip Jana, Rudra P SarkarAbstract:In this paper we give a simpler proof of the $L^p$-Schwartz Space isomorphism $(0< p\leq 2)$ under the Fourier transform for the class of functions of left $\delta$-type on a Riemannian Symmetric Space of rank one. Our treatment rests on Anker's \cite{A} proof of the corresponding result in the case of left $K$-invariant functions on $X$. Thus we give a proof which relies only on the Paley--Wiener theorem.
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on the schwartz Space isomorphism theorem for rank one Symmetric Space
Proceedings Mathematical Sciences, 2007Co-Authors: Joydip Jana, Rudra P SarkarAbstract:In this paper we give a simpler proof of the Lp-Schwartz Space isomorphism (0 < p ≤ 2) under the Fourier transform for the class of functions of left δ-type on a Riemannian Symmetric Space of rank one. Our treatment rests on Anker’s [2] proof of the corresponding result in the case of left K-invariant functions on X. Thus we give a proof which relies only on the Paley-Wiener theorem.
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beurling s theorem and characterization of heat kernel for riemannian Symmetric Spaces of noncompact type
Canadian Mathematical Bulletin, 2007Co-Authors: Rudra P Sarkar, Jyoti SenguptaAbstract:We prove Beurling's theorem for rank 1 Riemannian Symmetric Spaces and relate its consequences with the characterization of the heat kernel of the Symmetric Space.
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beurling s theorem and characterization of heat kernel for riemannian Symmetric Spaces of noncompact type
arXiv: Functional Analysis, 2005Co-Authors: Rudra P Sarkar, Jyoti SenguptaAbstract:We prove Beurling's theorem for rank 1 Riemmanian Symmetric Spaces and relate it to the characterization of the heat kernel of the Symmetric Space.
David M Schmidtt - One of the best experts on this subject based on the ideXlab platform.
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supersymmetry flows semi Symmetric Space sine gordon models and the pohlmeyer reduction
Journal of High Energy Physics, 2011Co-Authors: David M SchmidttAbstract:We study the extended superSymmetric integrable hierarchy underlying the Pohlmeyer reduction of superstring sigma models on semi-Symmetric superSpaces F/G. This integrable hierarchy is constructed by coupling two copies of the homogeneous integrable hierarchy associated to the loop Lie superalgebra extension \( \hat{\mathfrak{f}} \) of the Lie superalgebra \( \mathfrak{f} \) of F and this is done by means of the algebraic dressing technique and a Riemann-Hilbert factorization problem. By using the Drinfeld-Sokolov procedure we construct explicitly, a set of 2D spin ± 1/2 conserved supercharges generating supersymmetry flows in the phase Space of the reduced model. We introduce the bi-Hamiltonian structure of the extended homogeneous hierarchy and show that the two brackets are of the Kostant-Kirillov type on the co-adjoint orbits defined by the light-cone Lax operators L±. By using the second symplectic structure, we show that these supersymmetries are Hamiltonian flows, we compute part of the supercharge algebra and find the superSymmetric field variations they induce. We also show that this second Poisson structure coincides with the canonical Lorentz-invariant symplectic structure of the WZNW model involved in the Lagrangian formulation of the extended integrable hierarchy, namely, the semi-Symmetric Space sine-Gordon model (SSSSG), which is the Pohlmeyer reduced action functional for the transverse degrees of freedom of superstring sigma models on the cosets F/G. We work out in some detail the Pohlmeyer reduction of the AdS2 × S2 and the AdS3 × S3 superstrings and show that the new conserved supercharges can be related to the supercharges extracted from 2D superSpace. In particular, for the AdS2 × S2 example, they are formally the same.
Filip Blaschke - One of the best experts on this subject based on the ideXlab platform.
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cotangent bundle over hermitian Symmetric Space e 7 e 6 u 1 from projective superSpace
Journal of High Energy Physics, 2013Co-Authors: Masato Arai, Filip BlaschkeAbstract:We construct an $\mathcal{N}=2$ superSymmetric sigma model on the cotangent bundle over the Hermitian Symmetric Space E 7 /(E 6 × U(1)) in the projective superSpace formalism, which is a manifest $\mathcal{N}=2$ off-shell superfield formulation in four-dimensional Spacetime. To obtain this model we elaborate on the results developed in arXiv:0811.0218 and present a new closed formula for the cotangent bundle action, which is valid for all Hermitian Symmetric Spaces. We show that the structure of the cotangent bundle action is closely related to the analytic structure of the Kahler potential with respect to a uniform rescaling of coordinates.
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cotangent bundle over hermitian Symmetric Space e_7 e_6 times u 1 from projective superSpace
arXiv: High Energy Physics - Theory, 2012Co-Authors: Masato Arai, Filip BlaschkeAbstract:We construct an $\cN=2$ superSymmetric sigma model on the cotangent bundle over the Hermitian Symmetric Space $E_7/(E_6\times U(1))$ in the projective superSpace formalism, which is a manifest $\cN=2$ off-shell superfield formulation in four-dimensional Spacetime. To obtain this model we elaborate on results developed in arXiv:0811.0218 and present a new closed formula for the cotangent bundle action, which is valid for all Hermitian Symmetric Spaces. We show that the structure of cotangent bundle action is intimately related to the analytic structure of the K\"ahler potential with respect to a uniform rescaling of coordinates.
