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Logarithmic intertwining operators and genus-one correlation functions.

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TitleInfo
Title
Logarithmic intertwining operators and genus-one correlation functions.
Name (type = personal)
NamePart (type = family)
Fiordalisi
NamePart (type = given)
Francesco
DisplayForm
Francesco Fiordalisi
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
HUANG
NamePart (type = given)
YI-ZHI
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YI-ZHI HUANG
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Advisory Committee
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chair
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NamePart (type = family)
Lepowsky
NamePart (type = given)
James
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James Lepowsky
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Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Carbone
NamePart (type = given)
Lisa
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Lisa Carbone
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Milas
NamePart (type = given)
Antun
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Antun Milas
Affiliation
Advisory Committee
Role
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outside member
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NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2015
DateOther (qualifier = exact); (type = degree)
2015-05
CopyrightDate (encoding = w3cdtf); (qualifier = exact)
2015
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
We develop the theory of modular invariance for logarithmic intertwining operators. We construct and study genus-one correlation functions for logarithmic intertwining operators between generalized modules over a quasi-rational vertex operator algebra V . We consider generalized V -modules which admit a right action of some associative algebra P, and intertwining operators between modules in this class which commute with the action of P (P -intertwining operators). We obtain duality properties, i.e., suitable associativity and commutativity properties, for P -intertwining operators. Using the concept of pseudotrace introduced by Miyamoto, we define formal q-traces of products of P -intertwining operators, and obtain certain identities for these formal series. This allows us to show that the formal q-traces satisfy a system of differential equations with regular singular points, and therefore are absolutely convergent in a suitable region and can be extended to yield multivalued analytic functions, called genus-one correlation functions. Furthermore, we show that the space of solutions of these differential equations is invariant under the action of the modular group. We obtain a characterization of symmetric functions on bimodules over associative algebras in terms of pseudotraces of certain “bimodule actions”. We conclude by sketching the steps by which these results can be used to obtain a full modular invariance theorem for the genus-one correlation functions at least when the central charge is not 0. This modular invariance generalizes the full modular invariance theorem by Huang in the rational case. Miyamoto was the first to obtain a partial result that does not involve logarithmic intertwining operators or even intertwining operators. This modular invariance has been a conjecture for many years.
Subject (authority = RUETD)
Topic
Mathematics
Subject (authority = ETD-LCSH)
Topic
Correlation (Statistics)
Subject (authority = ETD-LCSH)
Topic
Operator algebras
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_6358
PhysicalDescription
Form (authority = gmd)
electronic resource
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application/pdf
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text/xml
Extent
1 online resource (vi, 72 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Francesco Fiordalisi
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3Z60QW6
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Fiordalisi
GivenName
Francesco
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2015-04-14 18:07:29
AssociatedEntity
Name
Francesco Fiordalisi
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
RightsEvent
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2015-05-31
DateTime (encoding = w3cdtf); (qualifier = exact); (point = end)
2015-11-30
Type
Embargo
Detail
Access to this PDF has been restricted at the author's request. It will be publicly available after November 30th, 2015.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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ETD
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windows xp
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