Majorana Fermion Quantum Mechanics for Higher Rank Tensors

We study quantum mechanical models in which the dynamical degrees of freedom are real fermionic tensors of rank five and higher. They are the non-random counterparts of the Sachdev-Ye-Kitaev (SYK) models where the Hamiltonian couples six or more fermions. For the tensors of rank five, there is a unique $O(N)^5$ symmetric sixth-order Hamiltonian leading to a solvable large $N$ limit dominated by the melonic diagrams. We solve for the complete energy spectrum of this model when $N=2$ and deduce exact expressions for all the eigenvalues. The subset of states which are gauge invariant exhibit degeneracies related to the discrete symmetries of the gauged model. We also study quantum chaos properties of the tensor model and compare them with those of the $q=6$ SYK model. For $q>6$ there is a rapidly growing number of $O(N)^{q-1}$ invariant tensor interactions. We focus on those of them that are maximally single-trace - their stranded diagrams stay connected when any set of $q-3$ colors is erased. We present a general discussion of why the tensor models with maximally single-trace interactions have large $N$ limits dominated by the melonic diagrams. We solve the large $N$ Schwinger-Dyson equations for the higher rank Majorana tensor models and show that they match those of the corresponding SYK models exactly. We also study other gauge invariant operators present in the tensor models.Comment: 36 pages, 19 figures, 2 tables, v3: some clarifications and references adde

Conformal Fixed Points of Unidentified Gauge Theories

In this article we discuss gauge/strings correspondence based on the non-critical strings. With this goal we present several remarkable sigma models with the AdS target spaces. The models have kappa symmetry and are completely integrable. The radius of the AdS space is fixed and thus they describe isolated fixed points of gauge theories in various dimensionsComment: 14 page

An Exact Bosonization Rule for c=1 Noncritical String Theory

We construct a string field theory for c=1 noncritical strings using the loop variables as the string field. We show how one can express the nonrelativistic free fermions which describes the theory, in terms of these string fields.Comment: 17 pages, to appear in JHE

Absorption of dilaton s-wave in type 0B string theory

We find the absorption probability of dilaton field in type 0B string theory. Since the background solutions are of the form $AdS_5 \times S^5$ on both regions, we use the semiclassical formalism adopted in type IIB theory to find the absorption cross section. The background tachyon field solution was used as a reference to relate the solutions of the two regions. We also consider the possible corrections to absorption probability and the $\ln(\ln z)$ form of the correction is expected as in the calculation of the confinement solution.Comment: minor corrections, reference added, version to appear PR

Absorption by Threebranes and the AdS/CFT Correspondence

In the first part of this talk I discuss two somewhat different supergravity approaches to calculating correlation functions in strongly coupled Yang-Mills theory. The older approach relates two-point functions to cross-sections for absorption of certain incident quanta by threebranes. In this approach the normalization of operators corresponding to the incident particles is fixed unambiguously by the D3-brane DBI action. By calculating absorption cross-sections of all partial waves of the dilaton we find corresponding two-point functions at strong `t Hooft coupling and show that they are identical to the weak coupling results. The newer approach to correlation functions relates them to boundary conditions in AdS space. Using this method we show that for a certain range of negative mass-squared there are two possible operator dimensions corresponding to a given scalar field in AdS, and indicate how to calculate correlation functions for either of these choices. In the second part of the talk I discuss an example of AdS/CFT duality which arises in the context of type 0 string theory. The CFT on N coincident electric and magnetic D3-branes is argued to be stable for sufficiently weak `t Hooft coupling. It is suggested that its transition to instability at a critical coupling is related to singularity of planar diagrams.Comment: 14 pages, LaTeX; Talk at Strings '99, Potsdam, German

On Tunnelling In Two-Throat Warped Reheating

We revisit the energy transfer necessary for the warped reheating scenario in a two-throat geometry. We study KK mode wavefunctions of the full two-throat system in the Randall--Sundrum (RS) approximation and find an interesting subtlety in the calculation of the KK mode tunnelling rate. While wavepacket tunnelling is suppressed unless the Standard Model throat is very long, wavefunctions of modes localized in different throats have a non-zero overlap and energy can be transferred between the throats by interactions between such KK modes. The corresponding decay rates are calculated and found to be faster than the tunnelling rates found in previously published works. However, it turns out that the imaginary parts of the mode frequencies, induced by the decay, slow the decay rates themselves down. The self-consistent decay rate turns out to be given by the plane wave tunnelling rate considered previously in the literature. We then discuss mechanisms that may enhance the energy transfer between the throats over the RS rates. In particular, we study models in which the warp factor changes in the UV region less abruptly than in the RS model, and find that it is easy to build phenomenological models in which the plane wave tunnelling rate, and hence the KK mode interaction rates, are enhanced compared to the standard RS setup.Comment: 27 pages + appendices, 5 figures, latex. v2: Discussion of decay in Section 4 changed: the most dangerous graviton amplitudes are zero, the results are now more positive for the warped reheating scenario; typos fixed, discussion cleaned up. v3:corrections in Section 5 (decay rates slowed down), mild changes of overall conclusion

Gauge/Gravity Duality and Warped Resolved Conifold

We study supergravity backgrounds encoded through the gauge/string correspondence by the SU(N) \times SU(N) theory arising on N D3-branes on the conifold. As discussed in hep-th/9905104, the dynamics of this theory describes warped versions of both the singular and the resolved conifolds through different (symmetry breaking) vacua. We construct these supergravity solutions explicitly and match them with the gauge theory with different sets of vacuum expectation values of the bi-fundamental fields A_1, A_2, B_1, B_2. For the resolved conifold, we find a non-singular SU(2)\times U(1)\times U(1) symmetric warped solution produced by a stack of D3-branes localized at a point on the blown-up 2-sphere. It describes a smooth RG flow from AdS_5 \times T^{1,1} in the UV to AdS_5 \times S^5 in the IR, produced by giving a VEV to just one field, e.g. B_2. The presence of a condensate of baryonic operator det B_2 is confirmed using a Euclidean D3-brane wrapping a 4-cycle inside the resolved conifold. The Green's functions on the singular and resolved conifolds are central to our calculations and are discussed in some detail.Comment: 22 pages, 2 figures, v2 added note on wrapped euclidean D3 brane, other minor correction

Emergent Quantum Near-Criticality from Baryonic Black Branes

We find new black 3-brane solutions describing the "conifold gauge theory" at nonzero temperature and baryonic chemical potential. Of particular interest is the low-temperature limit where we find a new kind of weakly curved near-horizon geometry; it is a warped product AdS_2 x R^3 x T^{1,1} with warp factors that are powers of the logarithm of the AdS radius. Thus, our solution encodes a new type of emergent quantum near-criticality. We carry out some stability checks for our solutions. We also set up a consistent ansatz for baryonic black 2-branes of M-theory that are asymptotic to AdS_4 x Q^{1,1,1}.Comment: 29 pages, 4 figures; v2 discussion of entropy revised, minor changes; v3 note added, minor improvements, version published in JHE