A New Anomaly-Free Gauged Supergravity in Six Dimensions

We present a new anomaly-free gauged N=1 supergravity model in six dimensions. The gauge group is E_7xG_2xU(1)_R, with all hyperinos transforming in the product representation {56,14). The theory admits monopole compactifications to R^4xS^2, leading to D=4 effective theories with broken supersymmetry and massless fermions.Comment: 9 pages, RevTeX

Complex marginal deformations of D3-brane geometries, their Penrose limits and giant gravitons

We apply the Lunin--Maldacena construction of gravity duals to beta-deformed gauge theories to a class of Type IIB backgrounds with U(1)^3 global symmetry, which include the multicenter D3-brane backgrounds dual to the Coulomb branch of N=4 super Yang-Mills and the rotating D3-brane backgrounds dual to the theory at finite temperature and chemical potential. After a general discussion, we present the full form of the deformed metrics for three special cases, which can be used for the study of various aspects of the marginally-deformed gauge theories. We also construct the Penrose limits of the solutions dual to the Coulomb branch along a certain set of geodesics and, for the resulting PP--wave metrics, we examine the effect of beta-deformations on the giant graviton states. We find that giant gravitons exist only up to a critical value of the sigma-deformation parameter, are not degenerate in energy with the point graviton, and remain perturbatively stable. Finally, we probe the sigma-deformed multicenter solutions by examining the static heavy-quark potential by means of Wilson loops. We find situations that give rise to complete screening as well as linear confinement, with the latter arising is an intriguing way reminiscent of phase transitions in statistical systems.Comment: 53 pages, 5 figures; v3: version to appear in Nucl. Phys.

Noncompact gaugings, chiral reduction and dual sigma models in supergravity

We show that the half-maximal SU(2) gauged supergravity with topological mass term admits coupling of an arbitrary number of n vector multiplets. The chiral circle reduction of the ungauged theory in the dual 2-form formulation gives N=(1,0) supergravity in 6D coupled to 3p scalars that parametrize the coset SO(p,3)/SO(p)x SO(3), a dilaton and (p+3) axions with p < n+1. Demanding that R-symmetry gauging survives in 6D is shown to put severe restrictions on the 7D model, in particular requiring noncompact gaugings. We find that the SO(2,2) and SO(3,1) gauged 7D supergravities give a U(1)_R, and the SO(2,1) gauged 7D supergravity gives an Sp(1)_R gauged chiral 6D supergravities coupled to certain matter multiplets. In the 6D models obtained, with or without gauging, we show that the scalar fields of the matter sector parametrize the coset SO(p+1,4)/SO(p+1)x SO(4), with the (p+3) axions corresponding to its abelian isometries. In the ungauged 6D models, upon dualizing the axions to 4-form potentials, we obtain coupling of p linear multiplets and one special linear multiplet to chiral 6D supergravity.Comment: 41 pages, late

Investigating the macroeconomic determinants of RDP house prices in South Africa

The main purpose of this study is to investigate the relationship between macroeconomic variables and South Africa's affordable housing market using basic multivariate regression analysis. This paper empirically examines whether increases in RDP house prices can be explained by or attributed to the movements in gross domestic product (GDP), prime lending rate (RATE), the stock market (JSE) and inflation (CPI). As an exploratory paper in nature, data of RDP resales prices from eight major metropolitan cities in South Africa was collected from the Centre of Affordable Housing Finance (CAHF) for the period 2007 to 2015. The findings from the regression analysis show that only JSE is a key determinant of RDP housing prices in South Africa. Since there was no a statistically significant relationship that could be found between affordable housing price movements and GDP, RATE and CPI, this study suggests that hedonic variables should be used in future studies, as well as accounting for regional differences. Notwithstanding, since the resale of RDP homes is a new dimension in the real estate market and whose introduction is also still at its infancy in South Africa, an examination of the RDP home prices is important to the financiers (financial institutions), investors, housing authorities, the government and other interested stakeholders who might want to have an understanding of the factors that drive the prices of these homes in South Africa. The results from this study, therefore, play a role in informing these parties as they allow them to make better decisions in terms of whether to make financing available (financial institutions), policy formulation or direction (government) and whether to invest or sale (other stakeholders)

Stability of string configurations dual to quarkonium states in AdS/CFT

We extend our earlier work, regarding the perturbative stability of string configurations used for computing the interaction potential of heavy quarks within the gauge/gravity correspondence, to cover a more general class of gravity duals. We provide results, mostly based on analytic methods and corroborated by numerical calculations, which apply to strings in a general class of backgrounds that encompass boosted, spinning and marginally-deformed D3-brane backgrounds. For the case of spinning branes we demonstrate in a few examples that perturbative stability of strings requires strong conditions complementing those following by thermodynamic stability of the dual field theories. For marginally-deformed backgrounds, we find that even in the conformal case stability may require an upper value for the imaginary part of the deformation parameter, whereas in regions of the Coulomb branch where there exists linear confinement we find that there exist stable string configurations for certain ranges of values of this parameter. We finally discuss the case of open strings with fixed endpoints propagating in Rindler space, which turns out to have an exact classical-mechanical analog.Comment: 41 pages, 16 figures; v2: minor typos corrected, version to appear in Nucl. Phys.

Wilson loops in warped resolved deformed conifolds

We calculate quark-antiquark potentials using the relationship between the expectation value of the Wilson loop and the action of a probe string in the string dual. We review and categorize the possible forms of the dependence of the energy on the separation between the quarks. In particular, we examine the possibility of there being a minimum separation for probe strings which do not penetrate close to the origin of the bulk space, and derive a condition which determines whether this is the case. We then apply these considerations to the flavoured resolved deformed conifold background of Gaillard et al. We suggest that the unusual behaviour we observe in this solution is likely to be related to the IR singularity which is not present in the unflavoured case

Stability of strings dual to flux tubes between static quarks in N=4 SYM

Computing heavy quark-antiquark potentials within the AdS/CFT correspondence often leads to behaviors that differ from what one expects on general physical grounds and field-theory considerations. To isolate the configurations of physical interest, it is of utmost importance to examine the stability of the string solutions dual to the flux tubes between the quark and antiquark. Here, we formulate and prove several general statements concerning the perturbative stability of such string solutions, relevant for static quark-antiquark pairs in a general class of backgrounds, and we apply the results to N=4 SYM at finite temperature and at generic points of the Coulomb branch. In all cases, the problematic regions are found to be unstable and hence physically irrelevant.Comment: 43 pages, 18 figures; v3: typos correcte

Brane Gravitational Interactions from 6D Supergravity

We investigate the massive graviton contributions to 4D gravity in a 6D brane world scenario, whose bulk field content can include that of 6D chiral gauged supergravity. We consider a general class of solutions having 3-branes, 4D Poincare symmetry and axisymmetry in the internal space. We show that these contributions, which we compute analytically, can be independent of the brane vacuum energy as a consequence of geometrical and topological properties of the above-mentioned codimension two brane world. These results support the idea that in such models the gravitational interactions may be decoupled from the brane vacuum energy.Comment: 13 pages, 4 figure

Gauged D=7 Supergravity on the S**1/Z_2 Orbifold

We construct the most general couplings of a bulk seven-dimensional Yang-Mills-Einstein N=2 supergravity with a boundary six-dimensional chiral N=(0,1) theory of vectors and charged hypermultiplets. The boundary consists of two brane worlds sitting at the fixed points of an S^1/Z_2 compactification of the seven-dimensional bulk supergravity. The resulting 6D massless spectrum surviving the orbifold projection is anomalous. By introducing boundary fields at the orbifold fixed points, we show that all anomalies are cancelled by a Green-Schwarz mechanism. In addition, all couplings of the boundary fields to the bulk are completely specified by supersymmetry. We emphasize that there is no bulk Chern-Simons term to cancel the anomalies. The latter is traded for a Green-Schwarz term which emerges in the boundary theory after a duality transformation implemented to construct the bulk supergravity.Comment: LaTeX, 42 pages; typos corrected, reference added, version to appear in Phys. Rev.