Small Treatise on Spin-3/2 Fields and their Dual Spectral Functions

In this work we systematically study various aspects of spin-3/2 fields in a curved background. We mostly focus on a minimally coupled massive spin-3/2 field in arbitrary dimensions, and solve the equation of motion either explicitly or numerically in AdS, Schwarzschild-AdS and Reissner-Nordstr\"om-AdS backgrounds. Although not the main focus of this work, we also make a connection with the gravitino equation of motion in gauged supergravity. Motivated by the AdS/CFT correspondence, we emphasize calculational improvements and technical details of the dual spectral functions. We attempt to provide a coherent and comprehensive picture of the existing literature.Comment: 40 pages, 11 figures. V2: comments and references adde

Comments on Higher Rank Wilson Loops in N=2∗{\cal N}=2^*

For ${\cal N}=2^*$ theory with $U(N)$ gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with $n$ rows and $k$ columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigenvalue distributions in various regimes of parameters $(N,\lambda,n,k)$ where $\lambda$ is the 't Hooft coupling. In the large $N$ limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previously known results for the totally symmetry and totally antisymmetric representations. We also extensively discusss the ${\cal N}=4$ limit of the ${\cal N}=2^*$ theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. As a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.Comment: 28 pages, 4 figures. v2: References added. v3: More references, JHEP versio

Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity

The topologically twisted index for ABJM theory with gauge group $U(N)_k \times U(N)_{-k}$ has recently been shown, in the large-$N$ limit, to reproduce the Bekenstein-Hawking entropy of certain magnetically charged asymptotically AdS$_4$ black holes. We numerically study the index beyond the large-$N$ limit and provide evidence that it contains a subleading logarithmic term of the form $-1/2\log N$. On the holographic side, this term naturally arises from a one-loop computation. However, we find that the contribution coming from the near horizon states does not reproduce the field theory answer. We give some possible reasons for this apparent discrepancy.Comment: 17 pages, 2 figures, discussion improve

One-loop Structure of Higher Rank Wilson Loops in AdS/CFT

The half-supersymmetric Wilson loop in $\mathcal N=4$ SYM is arguably the central non-local operator in the AdS/CFT correspondence. On the field theory side, the vacuum expectation values of Wilson loops in arbitrary representations of $SU(N)$ are captured to all orders in perturbation theory by a Gaussian matrix model. Of prominent interest are the $k$-symmetric and $k$-antisymmetric representations, whose gravitational description is given in terms of D3- and D5-branes, respectively, with fluxes in their world volumes. At leading order in $N$ and $\lambda$ the agreement in both cases is exact. In this note we explore the structure of the next-to-leading order correction in the matrix model and compare with existing string theory calculations. We find agreement in the functional dependence on $k$ but a mismatch in the numerical coefficients.Comment: 5 pages, one figure. v2: A crucial minus sign acknowledged; agreement now claimed only at the functional level. Changes in abstract and tex

Holographic Duals of Flavored N=1 Super Yang-Mills: Beyond the Probe Approximation

We construct backreacted D3/D7 supergravity backgrounds which are dual to four-dimensional N=1 and N=2 supersymmetric Yang-Mills at large N_c with flavor quarks in the fundamental representation of SU(N_c). We take into account the backreaction of D7-branes on either AdS(5) x S(5) or AdS(5) x T^{1,1}, or more generically on backgrounds where the space transverse to the D3-branes is Kaehler. The construction of the backreacted geometry splits into two stages. First we determine the modification of the six-dimensional space transverse to the D3 due to the D7, and then we compute the warp factor due to the D3. The N=2 background corresponds to placing a single stack of N_f D7-branes in AdS(5) x S(5). Here the Kaehler potential is known exactly, while the warp factor is obtained in certain limits as a perturbative expansion. By placing another D7'probe in the backreacted D3/D7 background, we derive the effect of the D7-branes on the spectrum of the scalar fluctuations to first order in N_f. The two systems with N=1 supersymmetry that we discuss are D3/D7/D7' and D3/D7 on the conifold. In both cases, the Kaehler potential is obtained perturbatively in the number of D7-branes. We provide all the ingredients necessary for the computation of each term in the expansion, and in each case give the first few terms explicitly. Finally, we comment on some aspects of the dual gauge theories.Comment: 39 pp, no figures; v.2 section 2.2 modified, singularities clarifie

Central Extensions of Finite Heisenberg Groups in Cascading Quiver Gauge Theories

Many conformal quiver gauge theories admit nonconformal generalizations. These generalizations change the rank of some of the gauge groups in a consistent way, inducing a running in the gauge couplings. We find a group of discrete transformation that acts on a large class of these theories. These transformations form a central extension of the Heisenberg group, generalizing the Heisenberg group of the conformal case, when all gauge groups have the same rank. In the AdS/CFT correspondence the nonconformal quiver gauge theory is dual to supergravity backgrounds with both five-form and three-form flux. A direct implication is that operators counting wrapped branes satisfy a central extension of a finite Heisenberg group and therefore do not commute.Comment: 25 pages, 12 figure