335 research outputs found
Modular curvature for toric noncommutative manifolds
A general question behind this paper is to explore a good notion for
intrinsic curvature in the framework of noncommutative geometry started by
Alain Connes in the 80s. It has only recently begun (2014) to be comprehended
via the intensive study of modular geometry on the noncommutative two tori. In
this paper, we extend recent results on the modular geometry on noncommutative
two tori to a larger class of noncommutative manifolds: toric noncommutative
manifolds. The first contribution of this work is a pseudo differential
calculus which is suitable for spectral geometry on toric noncommutative
manifolds. As the main application, we derive a general expression for the
modular curvature with respect to a conformal change of metric on toric
noncommutative manifolds. By specializing our results to the noncommutative two
and four tori, we recovered the modular curvature functions found in the
previous works. An important technical aspect of the computation is that it is
free of computer assistance.Comment: 59 pages. The paper was reorganized from the previous versio
Three-dimensional topological field theory and symplectic algebraic geometry I
We study boundary conditions and defects in a three-dimensional topological
sigma-model with a complex symplectic target space X (the Rozansky-Witten
model). We show that boundary conditions correspond to complex Lagrangian
submanifolds in X equipped with complex fibrations. The set of boundary
conditions has the structure of a 2-category; morphisms in this 2-category are
interpreted physically as one-dimensional defect lines separating parts of the
boundary with different boundary conditions. This 2-category is a
categorification of the Z/2-graded derived category of X; it is also related to
categories of matrix factorizations and a categorification of deformation
quantization (quantization of symmetric monoidal categories). In the appendix
we describe a deformation of the B-model and the associated category of branes
by forms of arbitrary even degree.Comment: 76 pages, AMS-latex. v2: references, acknowledgments, and a
discussion of grading ambiguities have been adde
TT-deformations, AdS/CFT and correlation functions
A solvable irrelevant deformation of AdS3/CFT2 correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed. It consists of a single trace deformation of the boundary theory, which is inspired by the recent work on solvable TT¯ deformations of two-dimensional CFTs. Thought of as a worldsheet σ-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS3 in the IR and a linear dilaton vacuum of little string theory in the UV. The insertion of the operator that realizes the deformation in the correlation functions produces a logarithmic divergence, leading to the renormalization of the primary operators, which thus acquire an anomalous dimension. We compute this anomalous dimension explicitly, and this provides us with a direct way of determining the spectrum of the theory. We discuss this and other features of the correlation functions in presence of the deformation.Fil: Giribet, Gaston Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentin
Deformation and Contraction of Symmetries in Special Relativity
This dissertation gives an account of the fundamental principles underlying two conceptionally different ways of embedding Special Relativity into a wider context. Both of them root in the attempt to explore the full scope of the Relativity Postulate. The first approach uses Lie algebraic analysis alone, but already yields a whole range of alternative kinematics that are all in a quantifiable sense near to those in Special Relativity, while being rather far away in a qualitative way. The corresponding models for spacetime are seen to be four-dimensional versions of the prototypical planar geometries associated with the work of Cayley and Klein. The close relationship between algebraic and geometric methods displayed by these considerations is being substantialized in terms of light-like spacetime extensions. The second direction of departures from Special Relativity stresses and develops the algebraic view on spacetime by considering Hopf instead of Lie algebras as candidates for the description of kinematical transformations and hence spacetime symmetry. This approach is motivated by the belief in the existence of a quantum theory of gravity, and the assumption that such manifests itself in nonlinear modifications of the laws of Special Relativity at length scales comparable to the Planck length. The twofold character of this work, and the presentation of an example for the fully geometric character of a specific Hopf algebraic deformation of the PoincareI algebra, enable a conclusion that speculates on a possible relationship between the two developed viewpoints via the technique of nonlinear realizations. A non-perturbative approach to the latter is given which generalizes to all the considered geometries
A Quantum Bound-State Description of Black Holes
A relativistic framework for the description of bound states consisting of a
large number of quantum constituents is presented, and applied to black-hole
interiors. At the parton level, the constituent distribution, number and energy
density inside black holes are calculated, and gauge corrections are discussed.
A simple scaling relation between the black hole mass and constituent number is
established.Comment: Sections on asymptotic framework for bound states and composite
operator renormalization added. Derivation of main results presented in
greater detail. References added. Submitted to Nuclear Physics
Quantization of the Nonlinear Sigma Model Revisited
We revisit the subject of perturbatively quantizing the nonlinear sigma model
in two dimensions from a rigorous, mathematical point of view. Our main
contribution is to make precise the cohomological problem of eliminating
potential anomalies that may arise when trying to preserve symmetries under
quantization. The symmetries we consider are twofold: (i) diffeomorphism
covariance for a general target manifold; (ii) a transitive group of isometries
when the target manifold is a homogeneous space. We show that there are no
anomalies in case (i) and that (ii) is also anomaly-free under additional
assumptions on the target homogeneous space, in agreement with the work of
Friedan. We carry out some explicit computations for the -model. Finally,
we show how a suitable notion of the renormalization group establishes the
Ricci flow as the one loop renormalization group flow of the nonlinear sigma
model.Comment: 51 page
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