Topological string theory

About: Topological string theory is a research topic. Over the lifetime, 1206 publications have been published within this topic receiving 54758 citations.

Lyapunov exponents and Hodge theory

Abstract: We started from computer experiments with simple one-dimensional ergodic dynamical systems called interval exchange transformations. Correlators in these systems decay as a power of time. In the simplest non-trivial case the exponent is equal to 1/3. We found a formula connecting characteristic exponents with explicit integrals over moduli spaces of algebraic curves with additional structures. Moreover, these integrals can be interpreted as correlators in a topological string theory. Also a new analogy arose between ergodic theory and complex algebraic geometry.

The shapes of Dirichlet defects

Abstract: If the vacuum manifold of a field theory has the appropriate topological structure, the theory admits topological structures analogous to the D-branes of string theory, in which defects of one dimension terminate on other defects of higher dimension. The shapes of such defects are analyzed numerically, with special attention paid to the intersection regions. Walls (co-dimension 1 branes) terminating on other walls, global strings (co-dimension 2 branes) and local strings (including gauge fields) terminating on walls are all considered. Connections to supersymmetric field theories, string theory and condensed matter systems are pointed out.

Remarks on quiver gauge theories from open topological string theory

Abstract: We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A ∞-structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, we prove a general and simple formula for effective superpotentials.

Transverse structure of the QCD string

Abstract: The characterization of the transverse structure of the QCD string is discussed. We formulate a conjecture as to how the stress-energy tensor of the underlying gauge theory couples to the string degrees of freedom. A consequence of the conjecture is that the energy density and the longitudinal-stress operators measure the distribution of the transverse position of the string, to leading order in the string fluctuations, whereas the transverse-stress operator does not. We interpret recent numerical measurements of the transverse size of the confining string and show that the difference of the energy and longitudinal-stress operators is a particularly natural probe at next-to-leading order. Second, we derive the constraints imposed by open-closed string duality on the transverse structure of the string. We show that a total of three independent ``gravitational'' form factors characterize the transverse profile of the closed string, and obtain the interpretation of recent effective string theory calculations: the square radius of a closed string of length $\ensuremath{\beta}$ defined from the slope of its gravitational form factor, is given by $\frac{d\ensuremath{-}1}{2\ensuremath{\pi}\ensuremath{\sigma}}\mathrm{log} \frac{\ensuremath{\beta}}{4{r}_{0}}$ in $d$ space dimensions. This is to be compared with the well-known result that the width of the open string at midpoint grows as $\frac{d\ensuremath{-}1}{2\ensuremath{\pi}\ensuremath{\sigma}}\mathrm{log} \frac{r}{{r}_{0}}$. We also obtain predictions for transition form factors among closed-string states.