Related papers: On the Geometry on Antisymmetric Fields
Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial…
Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…
Supersymmetry, originally proposed in particle physics, refers to a dual relation that connects fermionic and bosonic degrees of freedom in a system. Recently, there has been considerable interest in applying the idea of supersymmetry to…
We use a Hodge decomposition and its generalization to non-abelian flat vector bundles to calculate the partition function for abelian and non- abelian BF theories in $n$ dimensions. This enables us to provide a simple proof that the…
We explain how to perform topological twisting of supersymmetric field theories in the language of factorization algebras. Namely, given a supersymmetric factorization algebra with a choice of a topological supercharge we construct an…
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…
The construction of field theories with space-time symmetries, including tensorial charges (i.e. of M-theory type), initiated in hep-th/9907011, is extended to include interaction. For SO(2,2) gravity in a tensorial space-time, with…
We develop a general framework for the description of anomalies using extended functorial field theories extending previous work by Freed and Monnier. In this framework, anomalies are described by invertible field theories in one dimension…
We consider the compactification of Matrix theory on tori with background antisymmetric tensor field. Douglas and Hull have recently discussed how noncommutative geometry appears on the tori. In this paper, we demonstrate the concrete…
I define topological twists of supersymmetric field theories in the case when the supercharges involved obey an ``open'' algebra. Using the Batalin-Vilkovisky field-antifield formalism, I construct twisted theories algorithmically from the…
In this note, we consider how the bundle geometry of field space interplays with the covariant phase space methods so as to allow to write results of some generality on the presymplectic structure of invariant gauge theories coupled to…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
This survey discusses our results and conjectures concerning supersymmetric field theories and their relationship to cohomology theories. A careful definition of supersymmetric Euclidean field theories is given, refining Segal's axioms for…
Considering a nonlinear charged black hole as a thermodynamics system, we study the geometric description of its phase transitions. Using the formalism of geometrothermodynamics we show that the geometry of the space of thermodynamic…
Six-dimensional N=(1,0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This…
In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out…
We introduce and study several new topological operads that should be regarded as nonsymmetric analogues of the operads of little 2-disks, framed little 2-disks, and Deligne-Mumford compactifications of moduli spaces of genus zero curves…
We report on the following highlights from among the many discoveries made in Noncommutative Geometry since year 2000: 1) The interplay of the geometry with the modular theory for noncommutative tori, 2) Advances on the Baum-Connes…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit…