Related papers: Topological fermion condensates from anomalies
We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete K\"{a}hler-Dirac equations. The…
We suggest a simple grand unified theory where the fifth dimensional coordinate is compactified on an $S_1/(Z_2 \times Z_2')$ orbifold. This model is based on the supersymmetric flipped $SU(5) \times U(1)$ grand unified theory, which can…
The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate…
We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations…
The formation of singularities in the three-dimensional Euler equation is investigated. This is done by restricting the number of Fourier modes to a set which allows only for local interactions in wave number space. Starting from an initial…
Cosmology struggles with the theoretical problems generated by the observed value and recent emergence of a cosmological constant, in the standard model of cosmology, i.e. the concordance model. We propose to provide a more natural…
Universal topological data of topologically ordered phases can be captured by topological quantum field theory in continuous space time by taking the limit of low energies and long wavelengths. While previous continuum field-theoretical…
Many bundle gerbes constructed in practice are either infinite-dimensional, or finite-dimensional but built using submersions that are far from being fibre bundles. Murray and Stevenson proved that gerbes on simply-connected manifolds,…
Consider a finite triangulation of a surface $M$ of genus $g$ and assume that spin-less fermions populate the edges of the triangulation. The quantum dynamics of such particles takes place inside the algebra of canonical anti-commutation…
These lectures on anomalies are relatively self-contained and intended for graduate students who are familiar with the basics of quantum field theory. We begin with several derivations of the abelian anomaly: anomalous transformation of the…
The axial anomaly arising from the fermion sector of $\U(N)$ or $\SU(N)$ reduced model is studied under a certain restriction of gauge field configurations (the ``$\U(1)$ embedding'' with $N=L^d$). We use the overlap-Dirac operator and…
Non-supersymmetric orbifolds of N=1 super Yang-Mills theories are conjectured to inherit properties from their supersymmetric parent. We examine this conjecture by compactifying the Z_2 orbifold theories on a spatial circle of radius R. We…
We show that the assumption of non-zero topological susceptibility of the vacuum in a fermion-free version of a theory, such as gravity or QCD, suffices to conclude the following: Once N massless fermion flavors are added to the theory,…
We derive a rigorous classification of topologically stable Fermi surfaces of non-interacting, discrete translation-invariant systems from electronic band theory, adiabatic evolution and their topological interpretations. For systems on an…
We give a description of the delocalized twisted cohomology of an orbifold and the Chern character of a twisted vector bundle in terms of supersymmetric Euclidean field theories. This includes the construction of a twist functor for…
Dirac fermions coupled to gauge fields can exhibit the chiral anomaly even on a finite spatial lattice. A careful description of this phenomenon yields new insights into the nature of spin-charge relations and on-site symmetries (symmetries…
A recent result of Bader, Gelander and Sauer shows that for manifolds of pinched negative curvature, the torsion part of the homology can be controlled by the volume. This is done by constructing an efficient simplicial model of the thick…
One proposal for deriving effective cosmological models from theories of quantum gravity is to view the former as a mean-field (hydrodynamic) description of the latter, which describes a universe formed by a 'condensate' of quanta of…
We prove that a locally compact space with an upper curvature bound is a topological manifold if and only if all of its spaces of directions are homotopy equivalent and not contractible. We discuss applications to homology manifolds, limits…
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…