On alpha'-corrections to D-brane solutions

TL;DR

The paper develops a systematic framework to compute leading alpha'-corrections to D-brane solutions arising from higher-derivative terms in the low-energy action. It presents three complementary methods—direct EOM derivation, Palatini formalism, and an effective one-dimensional action—to obtain corrected D3-brane solutions, using the tractable R^4 term as a toy model. For the D3-brane, the alpha'-corrections renormalize the mass and tension and shift the dilaton, while the charge remains unchanged, with the near-horizon geometry staying AdS_5 x S^5; full consistency with F_5-dependent terms is expected to restore no-force behavior. The framework extends to general electric p-branes via a reduced 1d action and discusses thermodynamics via Wald's formalism, highlighting how higher-derivative terms modify the Smarr-type relations and offering a path to include complete alpha'-corrections once the full higher-derivative action is known.

Abstract

We discuss the computation of the leading corrections to D-brane solutions due to higher derivative terms in the corresponding low energy effective action. We develop several alternative methods for analyzing the problem. In particular, we derive an effective one-dimensional action from which the field equations for spherically symmetric two-block brane solutions can be derived, show how to obtain first order equations, and discuss a few other approaches. We integrate the equations for extremal branes and obtain the corrections in terms of integrals of the evaluation of the higher derivative terms on the lowest order solution. To obtain completely explicit results one would need to know all leading higher derivative corrections which at present are not available. One of the known higher derivative terms is the R^4 term, and we obtain the corrections to the D3 brane solution due to this term alone. We note, however, that (unknown at present) higher terms depending on F_5 are expected to modify our result. We analyze the thermodynamics of brane solutions when such quantum corrections are present. We find that the R^4 term induces a correction to the tension and the electric potential of the D3 brane but not to its charge, and the tension is still proportional to the electric potential times the charge. In the near-horizon limit the corrected solution becomes AdS_5 \times S^5 with the same cosmological constant as the lowest order solution but a different value of the (constant) dilaton.