Related papers: Zero Modes and the Atiyah-Singer Index in Noncommu…
We show in a model-independent way that, in the background of a topological soliton or instanton that saturates a Bogomol'nyi bound, the fermion and boson excitation spectra of non-zero modes cancel at the one-loop level. This generalizes…
We study free open fermionic strings on a non-commutative phase space. Modified super-Virasoro algebras in both Ramond and Neveu-Schwarz sectors acquire non-commutativity anomalies, and this noncommutativity also breaks Lorentz symmetry and…
We extend the method of matrix partition to obtain explicitly the gauge field for noncommutative ADHM construction in some general cases. As an application of this method we apply it to the U(2) 2-instanton and get explicit result for the…
The Atiyah-Singer index theorem on a closed manifold is well understood and appreciated in physics. On the other hand, the Atiyah-Patodi-Singer index, which is an extension to a manifold with boundary, is physicist-unfriendly, in that it is…
We consider the dynamics of a probe fermion charged under a U(1) Maxwell field and a two form potential $B_{(2)}$ in a five dimensional gravity background. The gravity background is constructed from a new solution we find of type IIB…
We discuss instanton fermionic zero modes in the heterotic N=(0,2) modification of the CP(1) sigma model in two dimensions. By calculating its chiral anomaly we prove that the number of fermionic zero modes is same as in the standard…
Dirac fermions, subject to external magnetic fields and in the presence of mass orders that assume topologically nontrivial spatial textures such as domain wall and vortices, for example, bind robust midgap states at zero energy, the number…
We investigate the role of gauge and gravitational instantons in the context of the Swampland program. Our focus is on the global symmetry breaking they induce, especially in the presence of fermions. We first recall and make more precise…
We study an interacting ensemble of instantons at finite baryon chemical potential. We emphasize the importance of fermionic zero modes and calculate the fermion induced interaction between instantons at non-zero chemical potential. We show…
In five spacetime dimensions, instantons are finite energy, solitonic particles. We describe the dynamics of these objects in the presence of a Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons term induces a…
Motivated by the exotic phenomenology of certain quantum materials and recent advances in programmable quantum emulators, we here study fermions and bosons in $\mathbb Z_N$ lattice gauge theories. We introduce a family of exactly soluble…
A nonlinear sigma model is derived for the time development of a Bose-Einstein condensate composed of fermionic atoms. Spontaneous symmetry breaking of a Sp(2) symmetry in a coherent state path integral with anticommuting fields yields…
We introduce a simple method to find localized exact fermionic zero modes for any local fermionic action. The zero modes are attached to specific local gauge configurations. Examples are provided for staggered and Wilson fermion actions in…
Atiyah-Singer index theorem on a lattice without boundary is well understood owing to the seminal work by Hasenfratz et al. But its extension to the system with boundary (the so-called Atiyah- Patodi-Singer index theorem), which plays a…
We introduce a mathematician-friendly formulation of the physicist-friendly derivation of the Atiyah-Patodi-Singer index of our previous paper. Our viewpoint sheds some new light on the interplay among the Atiyah-Patodi-Singer boundary…
We investigate an extension of ideas of Atiyah-Patodi-Singer (APS) to a noncommutative geometry setting framed in terms of Kasparov modules. We use a mapping cone construction to relate odd index pairings to even index pairings with APS…
In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two dimensional compact manifold $S^2$ as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes…
We find a regular analytic 1st order deformation of the Klebanov-Strassler background. From the dual gauge theory point of view the deformation describes supersymmetry soft breaking gaugino mass terms. We calculate the difference in vacuum…
Instantons play a crucial role in understanding non-perturbative dynamics in quantum field theories, including those with spontaneously broken gauge symmetries. In the broken phase, finite-size instanton-like configurations are no longer…
The basic objects of the ADHM construction are reformulated in terms of elements of the $A_{\theta}(R^4)$ algebra of the noncommutative $R_{\theta}^4$ space. This new formulation of the ADHM construction makes possible the explicit calculus…