Homotopy Transfer and Effective Field Theory II: Strings and Double Field Theory

Double Field Theory of Type II Strings

We use double field theory to give a unified description of the low energy limits of type IIA and type IIB superstrings. The Ramond-Ramond potentials fit into spinor representations of the duality group O(D,D) and field-strengths are obtained by acting with the Dirac operator on the potentials. The action, supplemented by a Spin+(D,D)covariant self-duality condition on field strengths, reduces ...

Strings and Unified Field Theory

It is argued that string theory predicts unified field theory rather than general relativity coupled to matter fields. In unified field theory all the objects are geometrical, for strings the Kalb-Ramond matter field is identical to the asymmetric part of the metric except that the fields contribute to different sides of the field equations. The dilaton is related to the object of non-metricity.

Homotopy Gerstenhaber Algebras and Topological Field Theory

We prove that the BRST complex of a topological conformal field theory is a homotopy Gerstenhaber algebra, as conjectured by Lian and Zuckerman in 1992. We also suggest a refinement of the original conjecture for topological vertex operator algebras. We illustrate the usefulness of our main tools, operads and “string vertices” by obtaining new results on Vassiliev invariants of knots and double...

Renormalization and Effective Field Theory

Open Strings and 3d Topological Field Theory

In the perturbative formulation of string theory the partition function in the background of D-branes can be expanded as Z string = g,b g −2+2g+b s Z g,b. (1) Here Z g,b is the value of the diagram given by a Riemann surface of genus g with b boundary components. One way to compute the numbers Z g,b is to work in conformal gauge. In this gauge one obtains a conformal field theory (CFT) living o...