Lectures on the Langlands Program and Conformal Field Theory
Identifieur interne : 000078 ( Istex/Corpus ); précédent : 000077; suivant : 000079Lectures on the Langlands Program and Conformal Field Theory
Auteurs : Edward FrenkelSource :
Abstract
Abstract : These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. It has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum field theory and string theory. Indeed, both the Langlands correspondence and the dualities in physics have emerged as some sort of non-abelian Fourier transforms. Moreover, the so-called Langlands dual group introduced by R. Langlands in [1] that is essential in the formulation of the Langlands correspondence also plays a prominent role in the study of S-dualities in physics and was in fact also introduced by the physicists P. Goddard, J. Nuyts and D. Olive in the framework of four-dimensional gauge theory [2].
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DOI: 10.1007/978-3-540-30308-4_11
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<front><div type="abstract" xml:lang="en">Abstract : These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. It has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum field theory and string theory. Indeed, both the Langlands correspondence and the dualities in physics have emerged as some sort of non-abelian Fourier transforms. Moreover, the so-called Langlands dual group introduced by R. Langlands in [1] that is essential in the formulation of the Langlands correspondence also plays a prominent role in the study of S-dualities in physics and was in fact also introduced by the physicists P. Goddard, J. Nuyts and D. Olive in the framework of four-dimensional gauge theory [2].</div>
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<name type="personal"><namePart type="given">Bernard</namePart>
<namePart type="family">Julia</namePart>
<affiliation>LPTENS, 24 rue Lhomond, F-75005, Paris, France</affiliation>
<affiliation>E-mail: Bernard.Julia@lpt.ens.fr</affiliation>
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<name type="personal"><namePart type="given">Pierre</namePart>
<namePart type="family">Vanhove</namePart>
<affiliation>Service de Physique Théorique, CEA/Saclay, 24 rue Lhomond, F-91191, Gif-sur-Yvette, France</affiliation>
<affiliation>E-mail: pierre.vanhove@cern.ch</affiliation>
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<abstract lang="en">Abstract : These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. It has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum field theory and string theory. Indeed, both the Langlands correspondence and the dualities in physics have emerged as some sort of non-abelian Fourier transforms. Moreover, the so-called Langlands dual group introduced by R. Langlands in [1] that is essential in the formulation of the Langlands correspondence also plays a prominent role in the study of S-dualities in physics and was in fact also introduced by the physicists P. Goddard, J. Nuyts and D. Olive in the framework of four-dimensional gauge theory [2].</abstract>
<relatedItem type="host"><titleInfo><title>Frontiers in Number Theory, Physics, and Geometry II</title>
<subTitle>On Conformal Field Theories, Discrete Groups and Renormalization</subTitle>
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<name type="personal"><namePart type="given">Pierre</namePart>
<namePart type="family">Cartier</namePart>
<affiliation>I.H.E.S., 35 route de Chartres, F-91440, Bures-sur-Yvette, France</affiliation>
<affiliation>E-mail: cartier@ihes.fr</affiliation>
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</name>
<name type="personal"><namePart type="given">Pierre</namePart>
<namePart type="family">Moussa</namePart>
<affiliation>Service de Physique Théorique, CEA/Saclay, F-91191, Gif-sur-Yvette, France</affiliation>
<affiliation>E-mail: moussa@spht.saclay.cea.fr</affiliation>
<role><roleTerm type="text">editor</roleTerm>
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</name>
<name type="personal"><namePart type="given">Bernard</namePart>
<namePart type="family">Julia</namePart>
<affiliation>LPTENS, 24 rue Lhomond, F-75005, Paris, France</affiliation>
<affiliation>E-mail: Bernard.Julia@lpt.ens.fr</affiliation>
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<name type="personal"><namePart type="given">Pierre</namePart>
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<affiliation>Service de Physique Théorique, CEA/Saclay, 24 rue Lhomond, F-91191, Gif-sur-Yvette, France</affiliation>
<affiliation>E-mail: pierre.vanhove@cern.ch</affiliation>
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<topic authority="SpringerSubjectCodes" authorityURI="SCM25001">Number Theory</topic>
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<topic authority="SpringerSubjectCodes" authorityURI="SCP19005">Theoretical, Mathematical and Computational Physics</topic>
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<identifier type="DOI">10.1007/978-3-540-30308-4</identifier>
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<identifier type="BookChapterCount">16</identifier>
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<part><date>2007</date>
<detail type="part"><title>Part II: Discrete Groups and Automorphic Forms</title>
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<detail type="part"><number>Part II</number>
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<extent unit="pages"><start>387</start>
<end>533</end>
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