F-theory and orientifolds

Abstract

By analyzing F -theory on K3 near the orbifold limit of K3 we establish the equivalence between F -theory on K3 and an orientifold of type IIB on T 2 , which in turn, is related by a T-duality transformation to type I theory on T 2 . By analyzing the F -theory background away from the orbifold limit, we show that non-perturbative effects in the orientifold theory splits an orientifold plane into two planes, with non-trivial SL(2,Z) monodromy around each of them. The mathematical description of this phenomenon is identical to the Seiberg-Witten result for N=2 supersymmetric SU(2) gauge theory with four quark flavors. Points of enhanced gauge symmetry in the orientifold / F -theory are in one to one correspondence with the points of enhanced global symmetry in the Seiberg-Witten theory.

Localized modes at a D-brane—O-plane intersection and heterotic Alice strings

“…It can be made locally flat, but globally it still has a deficit angle. The compact case is convincingly argued by Sen [23] to be dual to Type I and heterotic with the gauge group broken to SO(32) → SO(8) 4 .…”

“…When this is done, the O7-plane splits nonperturbatively into two (p, q) branes. This was studied by Sen [23], who related the moduli space of the system to that of N = 2 Seiberg-Witten theory with four flavors [31]. The splitting can also be seen from the supergravity solutions of [26].…”

“…As we reviewed above, Sen [23] has shown that when separating the D7-branes from the O7-plane, the region near the O7-plane has e −Φ ∼ 1. Nonperturbative effects cause the O7-plane to be split into two SL(2, ) transformed 7-branes.…”

“…Around the orientifold plane there is an SL(2, ) monodromy S 2 = −½. This corresponds to the transformation Ω(−1) F L on closed string modes of the IIB theory, where Ω is worldsheet orientation reversal and (−1) F L flips the sign of all Ramond states on the left [23]. For the 3-3 strings it corresponds to Ω, which, for the massless modes amounts to complex conjugation of the U (N c ) representation and a 2 action on the string wavefunction.…”

A holographic computation of the central charges ofd= 4, 𝒩 = 2 SCFTs

“…A simple example is the low-energy theory living on N D3-branes in F-theory [5,6,7] compactified on K3, which sit at an F-theory singularity for which the dilaton is constant [8,9,10,11,12]. There are seven types of such singularities, denoted by H 0 , H 1 , H 2 , D 4 , E 6 , E 7 , E 8 according to the low-energy gauge theory on the singularity (which is A n for the H n -type singularities); this is a global symmetry in the SCFT on the D3-branes (the global symmetry of these theories contains in addition an SU (2) L symmetry, and an SU (2) R × U (1) R R-symmetry).…”