Anomalies and Tadpoles in Open/Closed String Duality

TL;DR

This paper explores how divergences in open and closed string channels relate in string duality, linking gauge theory anomalies to supergravity calculations through the analysis of tadpoles and anomalies.

Contribution

It demonstrates the mapping of logarithmic divergences between open and closed string channels, providing evidence for gauge anomalies derived from supergravity.

Findings

Logarithmic divergences in closed strings correspond to open string one-loop divergences.

Tadpoles in supergravity are related to gauge theory anomalies.

Open/closed string duality explains anomaly matching in gauge theories.

Abstract

We discuss the role played by the divergences appearing in the interaction between a fractional D3 brane dressed with an SU(N) gauge field and a stack of N fractional D3 branes on the orbifolds C^2/Z_2 and C^3/(Z_2 x Z_2). In particular we show that the logarithmic divergences in the closed string channel, interpreted as due to twisted massless tadpoles, are mapped, under open/closed string duality, in the logarithmic ones in the open string channel, due to the massless states circulating in the annulus diagram and corresponding to the one-loop divergences that one finds in the gauge theory living in the world volume of the brane. This result provides a quantitative evidence of why the chiral and scale anomalies of the supersymmetric and non conformal gauge theories supported by the world volume of the branes can be inferred from supergravity calculations.