We compute the Witten index of one-dimensional gauged linear sigma models with at least \( \mathcal{N} \) = 2 supersymmetry. In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral. It is subject to a change as the Fayet-Iliopoulos parameter is varied through the phase boundaries. The wall crossing formula is expressed as an integral at infinity of the Coulomb branch. The result is applied to many examples, including quiver quantum mechanics that is relevant for BPS states in d = 4 \( \mathcal{N} \) =2 theories.

We study baryons in a holographic model of QCD by Sakai and Sugimoto, realized as small instantons with fundamental string hairs. We introduce an effective field theory of the baryons in the five-dimensional setting, and show that the instanton interpretation implies a particular magnetic coupling. Dimensional reduction to four dimensions reproduces the usual chiral effective action, and, in particular, we estimate the axial coupling $g_A$ between baryons and pions and the magnetic dipole moments, both of which are proportional to $N_c$. We extrapolate to finite $N_c$ and discuss subleading corrections.

A non-perturbative confinement mechanism has been proposed to explain the fate of the unbroken gauge group on the worldvolume of annihilating D-brane–anti-D-brane pairs. In this paper, we examine this phenomenon closely from several different perspectives. Existence of the confinement mechanism is most easily seen by noticing that the fundamental string emerges as the confined electric flux string at the end of the annihilation process. After reviewing the confinement proposal in general, this is shown explicitly in the D2–anti-D2 case in the M-theory limit. Finally, we address the crucial issue of whether and how confinement occurs in the weakly coupled limit of string theory.

In string theory realizations of inflation, the endpoint of inflation is often brane-antibrane annihilation. We consider the processes of reheating of the standard model universe after brane inflation. We identify the channels of inflaton energy decay, cascading from tachyon annihilation through massive closed string loops, KK modes, and brane displacement moduli to the lighter standard model particles. Cosmological data constrains scenarios by putting stringent limits on the fraction of reheating energy deposited in gravitons and nonstandard sector massive relics. We estimate the energy deposited into various light degrees of freedom in the open and closed string sectors, the timing of reheating, and the reheating temperature. Production of gravitons is significantly suppressed in warped inflation. However, we predict a residual gravitational radiation background at the level ${\Omega }_{\mathrm{GW}}\sim {10}^{-8}$ of the present cosmological energy density. We also extend our analysis to multiple throat scenarios. A viable reheating would be possible in a single throat or in a certain subclass of multiple throat scenarios of the KKLMMT type inflation model, but overproduction of massive Kaluza-Klein (KK) modes poses a serious problem. The problem is quite severe if some inner manifold comes with approximate isometries (angular KK modes) or if there exists a throat of modest length other than the standard model throat, possibly associated with some hidden sector (low-lying KK modes).

The vector dominance of the electromagnetic form factors both for mesons and baryons arises naturally in holographic QCD, where both the number of colors and the ’t Hooft coupling are taken to be very large, offering a bona-fide derivation of the notion of vector dominance. The crucial ingredient for this is the infinite tower of vector mesons in the approximations made which share features that are characteristic of the quenched approximation in lattice QCD. We approximate the infinite sum by contributions from the lowest four vector mesons of the tower which turn out to saturate the charge and magnetic moment sum rules within a few percent and compute them totally free of unknown parameters for momentum transfers $Q^2\lesssim 1{\mathrm{GeV}}^2$. We identify certain observables that can be reliably computed within the approximations and others that are not, and discuss how the improvement of the latter can enable one to bring holographic QCD closer to QCD proper.