536,126 research outputs found
Analytic geometry over F_1 and the Fargues-Fontaine curve
This paper develops a theory of analytic geometry over the field with one
element. The approach used is the analytic counter-part of the Toen-Vaquie
theory of schemes over F_1, i.e. the base category relative to which we work
out our theory is the category of sets endowed with norms (or families of
norms). Base change functors to analytic spaces over Banach rings are studied
and the basic spaces of analytic geometry (like polydisks) are recovered as a
base change of analytic spaces over F_1. We end by discussing some applications
of our theory to the theory of the Fargues-Fontaine curve and to the ring Witt
vectors.Comment: Small corrections have been made in the last section of the paper and
some typos have been correcte
Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
We study marginal and relevant supersymmetric deformations of the N=4
super-Yang-Mills theory in four dimensions. Our primary innovation is the
interpretation of the moduli spaces of vacua of these theories as
non-commutative spaces. The construction of these spaces relies on the
representation theory of the related quantum algebras, which are obtained from
F-term constraints. These field theories are dual to superstring theories
propagating on deformations of the AdS_5xS^5 geometry. We study D-branes
propagating in these vacua and introduce the appropriate notion of algebraic
geometry for non-commutative spaces. The resulting moduli spaces of D-branes
have several novel features. In particular, they may be interpreted as
symmetric products of non-commutative spaces. We show how mirror symmetry
between these deformed geometries and orbifold theories follows from T-duality.
Many features of the dual closed string theory may be identified within the
non-commutative algebra. In particular, we make progress towards understanding
the K-theory necessary for backgrounds where the Neveu-Schwarz antisymmetric
tensor of the string is turned on, and we shed light on some aspects of
discrete anomalies based on the non-commutative geometry.Comment: 60 pages, 4 figures, JHEP format, amsfonts, amssymb, amsmat
EVH Black Holes, AdS3 Throats and EVH/CFT Proposal
Within class of generic black holes there are extremal black holes (with
vanishing Hawking temperature T) and vanishing horizon area Ah, but with finite
Ah/T ratio,the Extremal Vanishing Horizon (EVH) black holes. We study the near
horizon limit of a four dimensional EVH black hole solution to a generic
(gauged) Einstein-Maxwell dilaton theory and show that in the near horizon
limit they develop a throat which is a pinching orbifold limit of AdS3. This is
an extension of the well known result for extremal black holes the near horizon
limit of which contains an AdS2 throat. We show that in the near EVH near
horizon limit the pinching AdS3 factor turns to a pinching BTZ black hole and
that this near horizon limit is indeed a decoupling limit. We argue that the
pinching AdS3 or BTZ orbifold is resolved if the near horizon limit is
accompanied by taking the 4d Newton constant G4 to zero such that the
Bekenstein-Hawking entropy S = Ah/(4G4) remains finite. We propose that in this
limit the near horizon EVH black hole is dual to a 2d CFT. We provide pieces of
evidence in support of the EVH/CFT correspondence and comment on its connection
to the Kerr/CFT proposal and speculations how the EVH/CFT may be used to study
generic e.g. Schwarzchild-type black holes.Comment: 31 pages, 3 figures, JHEP styl
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