We study the covariance properties of the equations satisfied by the generating functions of the chiral operators R and T of supersymmetric SO(N)/Sp(N) theories with symmetric/antisymmetric tensors. It turns out that T is an affine connection. As such it cannot be integrated along cycles on Riemann surfaces. This explains the discrepancies observed by Kraus and Shigemori. Furthermore, by means ...

Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus, verifying the inclusion of these surfaces in the Grassmannian. In particular, a subset of the class of O HD surfaces can be identified with a subset of the ...

Interpreting the number of ramified covering of a Riemann surface by Riemann surfaces as the relative Gromov-Witten invariants and applying a gluing formula, we derive a recursive formula for the number of ramified covering of a Riemann surface by Riemann surface with elementary branch points and prescribed ramification type over a special point.

Teichmiiller theory for super Riemann surfaces is rigorously developed using the supermanifold theory" of Rogers. In the case of trivial topology in the soul directions, relevant for superstring applications, the following results are proven. The super Teichmiiller space is a complex super-orbifold whose body is the ordinary Teichmiiller space of the associated Riemann surfaces with spin struct...

Riemann surfaces are geometric constructions in complex analysis that may represent multi-valued holomorphic functions using multiple sheets of the complex plane. We show that the energy dispersion of surface states in topological semimetals can be represented by Riemann surfaces generated by holomorphic functions in the two-dimensional momentum space, whose constant height contours correspond ...

The moduli space Mg of compact Riemann surfaces of genus g has structure of orbifold and the set of singular points for such orbifold is the branch locus Bg. In this article we present some results related with the topology of Bg, the connectedness of Bg for g ≤ 8, the existence of isolated equisymmetric strata of a given dimension in Bg and finally the connectedness of the branch locus of the ...

These are some notes that I collected from my readings about Riemann surfaces. Most of the notes are based on Beardon’s book Primer on Riemann Surfaces. These notes will serve as my lecture notes for a 25 minute talk I am giving in my Algebraic Topology class. I was not able to cover the last section during the talk.

The moduli spaceMg of compact Riemann surfaces of genus g has orbifold structure, and the set of singular points of such orbifold is the branch locus Bg. For g 6≡ 3 mod 4, g ≥ 26, g 6= 37, there exists isolated strata corresponding to families of pentagonal Riemann surfaces.