Related papers: Noncommutative Deformation of Spinor Zero Mode and…
We introduce a functional that couples the nonlinear sigma model with a spinor field: $L=\int_M[|d\phi|^2+(\psi,\D\psi)]$. In two dimensions, it is conformally invariant. The critical points of this functional are called Dirac-harmonic…
Paradigme shift in gauge topology, from instantons to their constituents -- instanton-dyons -- has recently lead to very significant advances. Like instantons, they have fermionic zero modes, and their collectivization at sufficiently high…
Non-singular instantons are shown to exist on noncommutative R^4 even with a U(1) gauge group. Their existence is primarily due to the noncommutativity of the space. The relation between U(1) instantons on noncommutative R^4 and the…
We find exact, analytic solutions of the Dirac equation for a charged, massless fermion in the background of a charged, dilatonic black hole in AdS_5. The black hole descends from type IIB supergravity, where it describes D3-branes with…
The coupling of spin 0 and spin 1 external fields to Dirac fermions defines a theory which displays gauge chiral symmetry. Quantum mechanically, functional integration of the fermions yields the determinant of the Dirac operator, known as…
We employ the ADHM method to derive the moduli space of two instantons in U(1) gauge theory on a noncommutative space. We show by an explicit hyperK\"ahler quotient construction that the relative metric of the moduli space of two instantons…
In this paper we compute the deformations of Clarke-Oliveira's instantons on the Bryant-Salamon $Spin(7)$-Manifold. The Bryant-Salamon $Spin(7)$-Manifold -- the negative spinor bundle of $S^4$ -- is an asymptotically conical manifold where…
An anti-self-dual instanton solution in Yang-Mills theory on noncommutative ${\R}^4$ with an anti-self-dual noncommutative parameter is constructed. The solution is constructed by the ADHM construction and it can be treated in the framework…
We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series…
The Dirac spin liquid (DSL) is a two-dimensional (2D) fractionalized Mott insulator featuring massless Dirac spinon excitations coupled to a compact $U(1)$ gauge field, which allows for flux-tunneling instanton events described by magnetic…
Projections play crucial roles in the ADHM construction on noncommutative $\R^4$. In this article a framework for the description of equivalence relations between projections is proposed. We treat the equivalence of projections as ``gauge…
We present a fermion model characterized by an anticommuting-parameter shift symmetry. The Hamiltonian formulation exhibits a combination of first-class and second-class constraints. We derive the well-known Dirac equation by fixing the…
We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge non invariant quantity. This generalizes the R <--> 1/R symmetry in which momenta and…
We introduce and study tetrahedron instantons, which can be realized in string theory by D$1$-branes probing a configuration of intersecting D$7$-branes in flat spacetime with a proper constant $B$-field. Physically they capture instantons…
In this work we study the quantum and Klein-Gordon oscillators in non-commutative complex space. We show that the quantum oscillator in non-commutative complex space obeys an equation similar to the equation of motion of an electron with…
We show that the moduli space of the $(2,0)$ and little-string theories compactified on $T^3$ with R-symmetry twists is equal to the moduli space of U(1) instantons on a non-commutative $T^4$. The moduli space of $U(q)$ instantons on a…
We show that for a suitable class of ``Dirac-like'' operators there holds a Gluing Theorem for connected sums. More precisely, if $M_1$ and $M_2$ are closed Riemannian manifolds of dimension $n\ge 3$ together with such operators, then the…
On a compact spin manifold we study the space of Riemannian metrics for which the Dirac operator is invertible. The first main result is a surgery theorem stating that such a metric can be extended over the trace of a surgery of codimension…
In the absence of gravity, Coleman's theorem states that the $O(4)$-symmetric instanton solution, which is regular at the origin and exponentially decays at infinity, gives the lowest action. Perturbatively, this implies that any small…
Defects which appear in heterostructure junctions involving topological insulators are sources of gapless modes governing the low energy properties of the systems, as recently elucidated by Teo and Kane [Physical Review B82, 115120 (2010)].…