Dilaton tadpoles and D-brane interactions in compact spaces

TL;DR

The paper investigates the physical consequences of NS-NS tadpoles arising when supersymmetry is broken by D-branes and orientifold planes on compact spaces. It develops an electrostatic toy model and a bi-warped supergravity framework to derive consistency conditions, showing that a global tadpole induces a jellium-like background and renormalizes the background geometry, thereby generically breaking Poincaré invariance on brane directions. A key result is the proper definition of massless propagators in compact spaces that exclude the zero mode, yielding finite D-brane interactions and clarifying divergences that appear in naive image-sum calculations. The paper also presents concrete examples, including supersymmetric cases with harmonic-function solutions and the Sugimoto model with uncancelled NS-NS tadpoles, as well as T-duality that maps to dislocalized branes and smeared orientifolds, highlighting the broader implications for background consistency and cosmology in string compactifications.

Abstract

We analyse some physical consequences when supersymmetry is broken by a set of D-branes and/or orientifold planes in Type II string theories. Generically, there are global dilaton tadpoles at the disk level when the transverse space is compact. By taking the toy model of a set of electric charges in a compact space, we discuss two different effects appearing when global tadpoles are not cancelled. On the compact directions a constant term appears that allows to solve the equations of motion. On the non-compact directions Poincaré invariance is broken. We analyse some examples where the Poincaré invariance is broken along the time direction (cosmological models).After that, we discuss how to obtain a finite interaction between D-branes and orientifold planes in the compact space at the supergravity level.

Figures (5)

• Figure 1: On the left hand side we have represented the electrostatic potential of two opposite charges on a circle. As tadpole conditions are satisfied one gets linear dependence as expected. On the right side the tadpoles are not cancelled and one finds a quadratic dependence on the distance proportional to the tadpole.
• Figure 2: Propagator on a circle. At short distances the behaviour is like in non-compact space. At large distance should be modified to take into account that our space is compact.
• Figure 3: Dilaton behaviour.
• Figure 4: Ricci scalar for the Dudas-Mourad solution.
• Figure 5: Dilaton behaviour for different solutions depending on the dimension of the brane.