Related papers: Index theorem on $T^2/\mathbb{Z}_N$ orbifolds
We introduce the topologically twisted index for four-dimensional $\mathcal N=1$ gauge theories quantized on ${\rm AdS}_2 \times S^1$. We compute the index by applying supersymmetric localization to partition functions of vector and chiral…
We have focused on the topological structure of Cubic string field theory (CSFT). From the similarity of action between CSFT and Chern-Simons (CS) theory in three dimensions, we have investigated the quantity ${\cal N}=\pi^2/3\int…
Commonly, a two-dimensional topological insulator is characterized by non-zero Chern numbers associated with its band structure. In our work, we present the experimental demonstration of an anomalous topological insulator, for which the…
We derive an index theorem for the Dirac operator in the background of various topological excitations on an R^3 \times S^1 geometry. The index theorem provides more refined data than the APS index for an instanton on R^4 and reproduces it…
Magnetized orbifolds play an important role in compactifications of string theories and higher-dimensional field theories to four dimensions. Magnetic flux leads to chiral fermions, it can be a source of supersymmetry breaking and it is an…
We calculate the chiral anomaly in the neighbourhood of the fixed point space M_h which is constructed by the group action of a discrete symmetry h on a compact manifold M. The Feynman diagrams approach for the corresponding supersymmetric…
We show that the R/Z part of the analytically defined eta invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a…
It is shown that the twisted sector spectrum, as well as the associated Chern-Simons interactions, can be determined on M-theory orbifold fixed planes that do not admit gravitational anomalies. This is demonstrated for the seven-planes…
A counting formula for computing the number of (Majorana) zero modes bound to topological point defects is evaluated in a gradient expansion for systems with charge-conjugation symmetry. This semi-classical counting of zero modes is applied…
The Atiyah-Singer index theorem, a landmark achievement of the early 1960s, brings together ideas in analysis, geometry, and topology. We recount some antecedents and motivations; various forms of the theorem; and some of its implications,…
In [Wu], the noncommutative Atiyah-Patodi-Singer index theorem was proved. In this paper, we extend this theorem to the equivariant case.
Using the Atiyah-Singer index theorem, we formally compute gravitational anomalies for fermionic higher-spin fields in two, six and ten dimensions, as well as the U(1) mixed gauge-gravitational anomaly in four dimensions. In all cases,…
The Chern number, nu, as a topological invariant that identifies the winding of the ground state in the particle-hole space, is a definitive theoretical signature that determines whether a given superconducting system can support Majorana…
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…
The two-loop chiral measure for superstring theories compactified on $\bZ_2$ reflection orbifolds is constructed from first principles for even spin structures. This is achieved by a careful implementation of the chiral splitting procedure…
We consider compactifications of the matrix model of M-theory on $S^1/Z_2\times T^d$ for $d>0$, and interpret them as orbifolds of the supersymmetric U(N) Yang-Mills theory on $R\times T^{d+1}$. The orbifold group acts both on the gauge…
By work of Kirby-Siebenmann \cite{KirbySiebenmann} and Kervaire-Milnor \cite{KervaireMilnor}, there are only finitely many smooth manifolds homeomorphic to a given closed topological manifold. A construction involving Whitehead torsion…
We propose an upper bound on the Atiyah-Singer index in the effective action of string theory. For $E_8 \times E_8^\prime$ and $SO(32)$ heterotic string theories on smooth Calabi-Yau threefolds with line bundles, we find that the tadpole…
We show that the moduli space of nonnegatively curved metrics on each member of a large class of 2-connected 7-manifolds, including each smooth manifold homeomorphic to $S^7$, has infinitely many connected components. The components are…
We study Z2-orbifolds of 11-dimensional M-theory on tori of various dimensions. The most interesting model (besides the known S1/Z2 case) corresponds to T5/Z2, for which we argue that the resulting six-dimensional theory is equivalent to…