Quantum parameter space in super Yang-Mills, II

In [1] (hep-th/0211069), the author has discussed the quantum parameter space of the N=1 super Yang-Mills theory with one adjoint Higgs field Phi, tree-level superpotential W_tree = m (Phi^2)/2 + g (Phi^3)/3$, and gauge group U(Nc). In particular, full details were worked out for U(2) and U(3). By discussing higher rank gauge groups like U(4), for which the classical parameter space has a large number of disconnected components, we show that the phenomena discussed in [1] are generic. It turns out that the quantum space is connected. The classical components are related in the quantum theory either through standard singularities with massless monopoles or by branch cuts without going through any singularity. The branching points associated with the branch cuts correspond to new strong coupling singularities, which are not associated with vanishing cycles in the geometry, and at which glueballs can become massless. The transitions discussed recently by Cachazo, Seiberg and Witten are special instances of those phenomena.Comment: 12 pages including 2 large figure

Slalom in complex time: emergence of low-energy structures in tunnel ionization via complex time contours

The ionization of atoms by strong, low-frequency fields can generally be described well by assuming that the photoelectron is, after the ionization step, completely at the mercy of the laser field. However, certain phenomena, like the recent discovery of low-energy structures in the long-wavelength regime, require the inclusion of the Coulomb interaction with the ion once the electron is in the continuum. We explore the first-principles inclusion of this interaction, known as analytical R-matrix theory, and its consequences on the corresponding quantum orbits. We show that the trajectory must have an imaginary component, and that this causes branch cuts in the complex time plane when the real trajectory revisits the neighbourhood of the ionic core. We provide a framework for consistently navigating these branch cuts based on closest-approach times, which satisfy the equation $\mathbf{r}(t) \cdot \mathbf{v}(t) = 0$ in the complex plane. We explore the geometry of these roots and describe the geometrical structures underlying the emergence of LES in both the classical and quantum domains.Comment: Supplementary information at http://episanty.github.io/Slalom-in-complex-time

Geometrically Induced Phase Transitions at Large N

Utilizing the large N dual description of a metastable system of branes and anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau threefold, we study phase transitions induced by changing the positions of the S^2's. At leading order in 1/N the effective potential for this system is computed by the planar limit of an auxiliary matrix model. Beginning at the two loop correction, the degenerate vacuum energy density of the discrete confining vacua split, and a potential is generated for the axion. Changing the relative positions of the S^2's causes discrete jumps in the energetically preferred confining vacuum and can also obstruct direct brane/anti-brane annihilation processes. The branes must hop to nearby S^2's before annihilating, thus significantly increasing the lifetime of the corresponding non-supersymmetric vacua. We also speculate that misaligned metastable glueball phases may generate a repulsive inter-brane force which stabilizes the radial mode present in compact Calabi-Yau threefolds.Comment: 47 pages, 7 figure

Phase Structure of a Brane/Anti-Brane System at Large N

We further analyze a class of recently studied metastable string vacua obtained by wrapping D5-branes and anti-D5-branes over rigid homologous S^2's of a non-compact Calabi-Yau threefold. The large N dual description is characterized by a potential for the glueball fields which is determined by an auxiliary matrix model. The higher order corrections to this potential produce a suprisingly rich phase structure. In particular, at sufficiently large 't Hooft coupling the metastable vacua present at weak coupling cease to exist. This instability can already be seen by an open string two loop contribution to the glueball potential. The glueball potential also lifts some of the degeneracy in the vacua characterized by the phases of the glueball fields. This generates an exactly computable non-vanishing axion potential at large N.Comment: v3: 55 pages, 11 figures, typos correcte

On Geometry and Matrix Models

We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.Comment: 24 page