(P,Q) webs in string theory.

摘要

String theory contains planar webs whose edges have rational slopes, and which we call (p,q) webs. The (p,q) webs can be realized either by string webs or by 5 brane webs in type IIB string theory. Despite its simple definition the web exhibits rich physical phenomena. The web is studied first in the abstract and then it is applied to 5d supersymmetric gauge theories and to the BPS spectrum of 4d N = 4 gauge theory, making use of the connection of field theories to the low energy effective action of branes in string theory. Some applications to algebraic geometry are described as well.; Many 5 dimensional N = 1 field theories can be realized by a brane configuration which is a 5 brane web. From it one can read the previously known vacuum structure and the mostly new BPS spectrum. The vacuum structure concepts which are realized through the web are local and global symmetries, the Coulomb branch, the prepotential, the integer parameter c, the roots of the Higgs branch and the Seiberg-Witten curve. The BPS spectrum is realized as string webs inside 5 brane webs. The sites in the charge lattice occupied by BPS states, and their spins are (partly) determined. The string webs include instantonic strings inside the 5 brane, which we call strips, and their junctions with strings which we call bends.; For the 4d N = 4 gauge theory webs bounded on D3 branes are found to represent many new 1/4 BPS monopoles. A systematic study of the BPS spectrum and spin is given. Marginal stability, which was previously unknown in N = 4, is found (not by the author). The fermionic zero modes of the web are determined. BPS monopoles in long multiplets are found. These states continuously deform to a non-BPS state as moduli are changed.