arXiv subjects
Publications and source records attributed to Girma Hailu.
The killing spinor of a linearly confining supergravity background previously proposed and argued to produce features of pure N=1 SU(N) gauge theory in four dimensions is constructed directly using the supersymmetry variations of the gravitino and the dilatino.
We propose a cosmological model of D3-brane universe on compact and stable supergravity background of wrapped D7-branes in type IIB string theory previously argued to be dual to pure N=1 SU(N) gauge theory in four dimensions. A model universe of order Planck size near the UV boundary dynamically flows toward the IR with constant total energy density and accelerating expansion followed by smooth transition to decelerating expansion and collides with the wrapped D7-branes at the IR boundary. The model addresses the horizon and flatness problems with most of the expansion produced during the decelerating expansion phase. The inflationary scenario is used to generate sources of inhomogeneities in the cosmic microwave background radiation and seeds for large scale structure formation from quantum fluctuations which exit the Hubble radius early during the accelerating expansion phase and the model addresses the inhomogeneity problem with red tilt in the power spectrum. We propose that the kinetic energy of the model universe is converted to matter and radiation by the collision followed by formation of baryons that stabilizes the model universe against gravitational force from the background at a finite distance from the IR boundary with the wrapped D7-branes serving as sources of color. Friedmann evolution then takes over with a positive cosmological constant term coming from the remaining potential energy density which is interpreted as dark energy. The magnitude of dark energy density is smaller than the total energy density during the flow by a ratio of the scale factor when the model universe appears in the UV to the scale factor at the moment of collision and stays constant while the matter-radiation density falls during Friedmann expansion.
Mass spectrum of 0++ glueballs is produced using a dual supergravity theory we proposed for pure N=1 SU(N) gauge theory in four dimensions in the large N limit in the IR. The glueball states are expressed in terms of Whittaker functions. The spectrum is discrete and a function whose roots give the masses is written. The ratios of the masses are independent of the parameters of the theory and comparison to recent non-supersymmetric large N lattice QCD data available for the lowest three states shows agreement to within five percent.
A supergravity background that produces linear confinement of quarks in four dimensions is presented.
We show that brane inflation is very sensitive to tiny sharp features in extra dimensions, including those in the potential and in the warp factor. This can show up as observational signatures in the power spectrum and/or non-Gaussianities of the cosmic microwave background radiation (CMBR). One general example of such sharp features is a succession of small steps in a warped throat, caused by Seiberg duality cascade using gauge/gravity duality. We study the cosmological observational consequences of these steps in brane inflation. Since the steps come in a series, the prediction of other steps and their properties can be tested by future data and analysis. It is also possible that the steps are too close to be resolved in the power spectrum, in which case they may show up only in the non-Gaussianity of the CMB temperature fluctuations and/or EE polarization. We study two cases. In the slow-roll scenario where steps appear in the inflaton potential, the sensitivity of brane inflation to the height and width of the steps is increased by several orders of magnitude comparing to that in previously studied large field models. In the IR DBI scenario where steps appear in the warp factor, we find that the glitches in the power spectrum caused by these sharp features are generally small or even unobservable, but associated distinctive non-Gaussianity can be large. Together with its large negative running of the power spectrum index, this scenario clearly illustrates how rich and different a brane inflationary scenario can be when compared to generic slow-roll inflation. Such distinctive stringy features may provide a powerful probe of superstring theory.
We find a dual gravity theory to pure confining N=1 supersymmetric SU(N) gauge theory in four dimensions which has the correct gauge coupling running in addition to reproducing the appropriate pattern of chiral symmetry breaking. It is constructed in type IIB string theory on R^{1,3} X R^1 X S^2 X S^3 background with N number of electric D5 and 2N number of magnetic D7-branes filling four dimensional spacetime and wrapping respectively two and four cycles.
We present a new gauge/gravity duality construction of the Klebanov-Strassler throat which takes corrections to the anomalous mass dimension proposed in [1] into account on the gauge theory side and both the dilaton and the axion run on the gravity side. The corresponding supergravity solutions are found using equations for type IIB flows with N=1 supersymmetry obtained in [2]. We find that magnetic couplings of the axion to D7-branes filling 4-d spacetime and wrapping 4-cycles at locations of duality transitions and invisible Dirac 8-branes whose worldvolume emanates from the worldvolume of the D7-branes are the sources for the runnings of the dilaton and the axion. Our construction provides the first explicit example of a gauge/gravity duality mapping with a running dilaton or a running axion which is an important component towards finding gravity duals to gauge theories with physically more interesting renormalization group flows such as pure confining gauge theories in four dimensions. The D7-branes also serve as gravitational source for Seiberg duality transitions. The supergravity background has distinct features which could be useful for constructing cosmological models and studying possibilities for probing stringy signatures from the early universe.
We write general and explicit equations which solve the supersymmetry transformations with two arbitrary complex-proportional Weyl spinors on $\mathcal{N}=1$ supersymmetric type IIB strings backgrounds with all R-R $F_1$, $F_3$, $F_5$ and NS-NS $H_3$ fluxes turned on using SU(3) structures. The equations are generalizations of the ones found for specific relations between the two spinors by Grana, Minasian, Petrini and Tomasiello in [1] and by Butti, Grana, Minasian, Petrini and Zaffaroni in [2]. The general equations allow to study systematically generic type IIB backgrounds with $\mathcal{N}=1$ supersymmetry. We then explore some specific classes of flows with constant axion, flows with constant dilaton, flows on conformally Calabi-Yau backgrounds, flows with imaginary self-dual 3-form flux, flows with constant ratio of the two spinors, the corresponding equations are written down and some of their features and relations are discussed.
We study corrections to the anomalous mass dimension and their effects in the Seiberg duality cascade in the Klebanov-Strassler throat, where $\mathcal{N}=1$ supersymmetric $SU(N+M)\times SU(N)$ gauge theory with bifundamental chiral superfields and a quartic tree level superpotential in four dimensions is dual to type IIB string theory on $AdS_5 \times T^{1,1}$ background. Analyzing the renormalization group flow of the couplings on the gauge theory side, we propose specific corrections to the anomalous mass dimension. Applying gauge/gravity duality, we then show that the corrections reveal structures on the supergravity side with steps appearing in the running of the fluxes and the metric. The "charges" at the steps provide a gravitational source for Seiberg duality transformations. The finiteness of these corrections suggests that the theory flows to a baryonic branch rather than to a confining branch. The cosmological implication of the duality cascade and the gauge/gravity duality on the brane inflationary scenario and the cosmic microwave background radiation is pointed out.
We solve $\mathcal{N}=1$ supersymmetric $A_{2}$ type $U(N)\times U(N)$ matrix models obtained by deforming $\mathcal{N}=2$ with symmetric tree level superpotentials of any degree exactly in the planar limit. These theories can be geometrically engineered from string theories by wrapping D-branes over Calabi-Yau threefolds and we construct the corresponding exact quantum geometries.
We discuss exact results for the full nonperturbative effective superpotentials of four dimensional $\mathcal{N}=1$ supersymmetric U(N) gauge theories with additional chiral superfield in the adjoint representation and the free energies of the related zero dimensional bosonic matrix models with polynomial potentials in the planar limit using the Dijkgraaf-Vafa matrix model prescription and integrating in and out. The exact effective superpotentials are produced including the leading Veneziano-Yankielowicz term directly from the matrix models. We also discuss how to use integrating in and out as a tool to do random matrix integrals in the large $N$ limit.
We study the quantum moduli spaces and dynamical superpotentials of four dimensional $SU(2)^r$ linear and ring moose theories with $\mathcal{N}=1$ supersymmetry and link chiral superfields in the fundamental representation. Nontrivial quantum moduli spaces and dynamical superpotentials are produced. When the moduli space is perturbed by generic tree level superpotentials, the vacuum space becomes discrete. The ring moose is in the Coulomb phase and we find two singular submanifolds with a nontrivial modulus that is a function of all the independent gauge invariants needed to parameterize the quantum moduli space. The massive theory near these singularities confines. The Seiberg-Witten elliptic curve that describes the quantum moduli space of the ring moose is produced.
Quantum moduli spaces of four dimensional $SU(2)^{r}$ linear and ring moose theories with $\mathcal{N}=1$ supersymmetry and link chiral superfields in the fundamental representation are produced starting from simple pure gauge theories of disconnected nodes.
We compute loop corrections to the effective action of a field theory on a five-dimensional $S_1/Z_2$ orbifold. We find that the quantum loop effects of interactions in the bulk produce infinite contributions that require renormalization by four-dimensional couplings on the orbifold fixed planes. Thus bulk couplings give rise to renormalization group running of brane couplings.
We note that orbifold boundary conditions that produce chiral fermion zero modes in compactified higher dimensional theories may distort scalar field vacuum expectation values, giving rise to nontrivial dependence on the extra dimensions. We illustrate this in a simple five dimensional model which has chiral fermion zero-modes stuck to fat branes. The model could provide a simple and explicit realization of the separation of quarks and leptons in the fifth dimension. We discuss the KK expansion in some detail. We find that there are in general non-zero-mode states stuck to the brane, like the chiral zero modes. We see explicitly the transition from states dominated by the internal structure of the fat brane to those dominated by the compactification.