Brane Theory Solitons

TL;DR

Brane Theory Solitons investigates how field-theoretic solitons emerge as a special limit of brane theories and how they generalize to brane dynamics through calibrations. The work develops a Hamiltonian framework for p-branes, showing that low-energy brane dynamics reduce to sigma-models with additional relativistic corrections, and identifies energy bounds tied to calibration forms. By analyzing sigma-model lumps and their minimization via Bogomol'nyi-type procedures, it connects holomorphic curves on Kähler/hyper-Kähler targets to finite-energy brane solitons and extends these ideas to M-theory constructions with M2/M5 branes and D-brane reductions. The epilogue situates brane theory as a non-gravitational, calibration-driven arena for solitons, with implications for brane-world gravity and AdS/CFT perspectives, highlighting a unifying viewpoint beyond conventional field theory.

Abstract

Field theories that describe {\sl small} fluctuations of branes are limits of `brane theories' that describe {\sl large} fluctuations. In particular, supersymmetric sigma-models arise in this way. These lectures discuss the soliton solutions of the associated `brane theories' and their relation to calibrations.