Elliptic Genera of Symmetric Products and Second Quantized Strings

In this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $M^N/S_N$ of a manifold $M$ to the partition function of a second quantized string theory on the space $M \times S^1$. The generating function of the...

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Detalles Bibliográficos
Autores principales: Dijkgraaf, Robbert, Moore, Gregory W., Verlinde, Erik P., Verlinde, Herman L.
Lenguaje:eng
Publicado: 1996
Materias:
Particle Physics - Theory
Acceso en línea:https://dx.doi.org/10.1007/s002200050087
http://cds.cern.ch/record/308863
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author Dijkgraaf, Robbert
Moore, Gregory W.
Verlinde, Erik P.
Verlinde, Herman L.
author_facet Dijkgraaf, Robbert
Moore, Gregory W.
Verlinde, Erik P.
Verlinde, Herman L.
author_sort Dijkgraaf, Robbert
collection CERN
description In this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $M^N/S_N$ of a manifold $M$ to the partition function of a second quantized string theory on the space $M \times S^1$. The generating function of these elliptic genera is shown to be (almost) an automorphic form for $O(3,2,\Z)$. In the context of D-brane dynamics, this result gives a precise computation of the free energy of a gas of D-strings inside a higher-dimensional brane.
id cern-308863
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1996
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spelling cern-3088632023-03-12T05:57:39Zdoi:10.1007/s002200050087http://cds.cern.ch/record/308863engDijkgraaf, RobbertMoore, Gregory W.Verlinde, Erik P.Verlinde, Herman L.Elliptic Genera of Symmetric Products and Second Quantized StringsParticle Physics - TheoryIn this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $M^N/S_N$ of a manifold $M$ to the partition function of a second quantized string theory on the space $M \times S^1$. The generating function of these elliptic genera is shown to be (almost) an automorphic form for $O(3,2,\Z)$. In the context of D-brane dynamics, this result gives a precise computation of the free energy of a gas of D-strings inside a higher-dimensional brane.In this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $M~N/S_N$ of a manifold $M$ to the partition function of a second quantized string theory on the space $M \times S~1$. The generating function of these elliptic genera is shown to be (almost) an automorphic form for $O(3,2,\Z)$. In the context of D-brane dynamics, this result gives a precise computation of the free energy of a gas of D-strings inside a higher-dimensional brane.hep-th/9608096CERN-TH-96-222ITFA-96-31YCTP-P16-96CERN-TH-96-222ITFA-96-31YCTP-P-96-16oai:cds.cern.ch:3088631996-08-15
spellingShingle Particle Physics - Theory
Dijkgraaf, Robbert
Moore, Gregory W.
Verlinde, Erik P.
Verlinde, Herman L.
Elliptic Genera of Symmetric Products and Second Quantized Strings
title Elliptic Genera of Symmetric Products and Second Quantized Strings
title_full Elliptic Genera of Symmetric Products and Second Quantized Strings
title_fullStr Elliptic Genera of Symmetric Products and Second Quantized Strings
title_full_unstemmed Elliptic Genera of Symmetric Products and Second Quantized Strings
title_short Elliptic Genera of Symmetric Products and Second Quantized Strings
title_sort elliptic genera of symmetric products and second quantized strings
topic Particle Physics - Theory
url https://dx.doi.org/10.1007/s002200050087
http://cds.cern.ch/record/308863
work_keys_str_mv AT dijkgraafrobbert ellipticgeneraofsymmetricproductsandsecondquantizedstrings
AT mooregregoryw ellipticgeneraofsymmetricproductsandsecondquantizedstrings
AT verlindeerikp ellipticgeneraofsymmetricproductsandsecondquantizedstrings
AT verlindehermanl ellipticgeneraofsymmetricproductsandsecondquantizedstrings

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