Related papers: Tetrahedral modular graph functions
Nonrelativistic open string theory is defined by a worldsheet theory that produces a Galilean invariant string spectrum and is described at low energies by a nonrelativistic Yang-Mills theory. We study T-duality transformations in the path…
The main result of this paper is the construction of a conformally covariant operator in two dimensions acting on scalar fields and containing fourth order derivatives. In this way it is possible to derive a class of Lagrangians invariant…
Heterotic string theory compactified on a K3 surface times T^2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the…
We present an analog to classic potential theory on weighted graphs. With nodes partitioned into exterior, boundary and interior nodes and an appropriate decomposition of the Laplacian, we define discrete analogues to the trace operators,…
To understand in detail the contribution of a world-sheet instanton to the superpotential in a heterotic string compactification, one has to understand the moduli dependence (bundle and complex structure moduli) of the one-loop determinants…
Following the idea of Refs.[1,2], the double-copy-like decomposition of exchanged internal states in the world-line limit of one-loop string amplitudes is systematically formulated and generalized to both bosonic and heterotic string…
By a recent observation, the Laplacians on the Riemannian manifolds the author used for isospectrality constructions are nothing but the Zeeman-Hamilton operators of free charged particles. These manifolds can be considered as prototypes of…
The stringy picture behind the integrable spin chains governing the evolution equations in Yang-Mills theory is discussed. It is shown that one-loop dilatation operator in N=4 theory can be expressed in terms of two-point functions on 2d…
In type II superstring theory, the vacuum amplitude at a given loop order $g$ can receive contributions from the boundary of the compactified, genus $g$ supermoduli space of curves $\overline{\mathfrak M}_g$. These contributions capture the…
The dilatation generator measures the scaling dimensions of local operators in a conformal field theory. In this thesis we consider the example of maximally supersymmetric gauge theory in four dimensions and develop and extend techniques to…
Modular graph forms are a class of modular covariant functions which appear in the genus-one contribution to the low-energy expansion of closed string scattering amplitudes. Modular graph forms with holomorphic subgraphs enjoy the…
Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…
This work deals with two types of Feynman integrals in perturbative quantum field theory: the 2-loop 2-point kite, with 5 arbitrary internal masses, and its completion by a sixth propagator, to give a 3-loop tetrahedral tadpole, with 6…
This is the second installment of a series of three papers in which we describe a method to determine higher-point correlation functions in one-loop open-superstring amplitudes from first principles. In this second part, we study worldsheet…
We lay out the foundations of the theory of second-order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: $(\Delta_n+V({\bf x}))\Psi=0$. Distinct families of…
We examine some features of the non-renormalizability induced through the use of low-energy effective Lagrangians in loop diagrams, in the context of a scalar model which is ultraviolet finite and partially soluble. In this framework, one…
The Laplace operator in infinite quantum waveguides (e.g., a bent strip or a twisted tube) often has a point-like eigenvalue below the essential spectrum that corresponds to a trapped eigenmode of finite L2 norm. We revisit this statement…
A worldsheet realization of the refined topological string is proposed in terms of physical string amplitudes that compute generalized N=2 F-terms of the form F_{g,n} W^{2g}Y^{2n} in the effective supergravity action. These terms involve…
We study the structure and dynamics of the infinite sequence of extensions of the Poincar{\'e} algebra whose method of construction was described in a previous paper [1]. We give explicitly the Maurer-Cartan (MC) 1-forms of the extended Lie…
Diagrammatic rules are developed for simplifying two-loop QED diagrams with propagators in a constant self-dual background field. This diagrammatic analysis, using dimensional regularization, is used to explain how the fully renormalized…