Higher loop nonplanar anomalous dimensions from symmetry

In this article we study the action of the one loop dilatation operator on operators with a classical dimension of order N . These operators belong to the su (2) sector and are constructed using two complex fields Y and Z . For these operators non-planar diagrams contribute already at the leading order in N and the planar and large N limits are distinct. The action of the one loop and the two loop dilatation operator reduces to a set of decoupled oscillators and factorizes into an action on the Z fields and an action on the Y fields. Direct computation has shown that the action on the Y fields is the same at one and two loops. In this article, using the su (2) symmetry algebra as well as structural features of field theory, we give compelling evidence that the factor in the dilatation operator that acts on the Y s is given by the one loop expression, at any loop order

Renormalization procedure for random tensor networks and the canonical tensor model

We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum gravity. The result is a generalization of the previous one concerning the relation between the Ising model on random networks and the canonical tensor model with . We also prove a general theorem that relates discontinuity of the renormalization-group flow and the phase transitions of random tensor networks

Hot attractors

The product of the areas of the event horizon and the Cauchy horizon of a non-extremal black hole equals the square of the area of the horizon of the black hole obtained from taking the smooth extremal limit. We establish this result for a large class of black holes using the second order equations of motion, black hole thermodynamics, and the attractor mechanism for extremal black holes. This happens even though the area of each horizon generically depends on the moduli, which are asymptotic values of scalar fields. The conformal field theory dual to the BTZ black hole facilitates a microscopic interpretation of the result. In addition, we demonstrate that certain quantities which vanish in the extremal case are zero when integrated over the region between the two horizons. We corroborate these conclusions through an analysis of known solutions

Attractive holographic c -functions

Using the attractor mechanism for extremal solutions in N = 2 $$\mathcal{N}=2$$ gauged supergravity, we construct a c -function that interpolates between the central charges of theories at ultraviolet and infrared conformal fixed points corresponding to anti-de Sitter geometries. The c -function we obtain is couched purely in terms of bulk quantities and connects two different dimensional CFTs at the stable conformal fixed points under the RG flow

Interpreting canonical tensor model in minisuperspace

Canonical tensor model is a theory of dynamical fuzzy spaces in arbitrary space–time dimensions. Examining its simplest case, we find a connection to a special case of minisuperspace model of general relativity in arbitrary dimensions. This is a first step in interpreting variables in canonical tensor model based on the known language of general relativity

Ising model on random networks and the canonical tensor model

We introduce a statistical system on random networks of trivalent vertices for the purpose of studying the canonical tensor model, which is a rank-three tensor model in the canonical formalism. The partition function of the statistical system has a concise expression in terms of integrals, and has the same symmetries as the kinematical ones of the canonical tensor model. We consider the simplest non-trivial case of the statistical system corresponding to the Ising model on random networks, and find that its phase diagram agrees with what is implied by regrading the Hamiltonian vector field of the canonical tensor model with $N=2$ as a renormalization group flow. Along the way, we obtain an explicit exact expression of the free energy of the Ising model on random networks in the thermodynamic limit by the Laplace method. This paper provides a new example connecting a model of quantum gravity and a random statistical system

Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS 4 /CFT 3

We study the duality between M-theory in AdS and the ABJM ChernSimons-matter theory with gauge group U( ) and level , taking large and of order 1. In this M-theoretic regime the lack of an explicit formulation of M-theory in AdS makes the gravity side difficult, while the CFT is strongly coupled and the planar approximation is not applicable. We focus on states on the gravity side with large angular momentum associated with a single plane of rotation in and identify their dual operators in the CFT. We show that natural approximation schemes arise on both sides thanks to the presence of the small parameter . On the AdS side, we use the matrix model of M-theory on the maximally supersymmetric pp-wave background with matrices of size . A perturbative treatment of this matrix model provides a good approximation to M-theory in AdS when . On the CFT side, we study the theory on with magnetic flux . A BornOppenheimer-type expansion arises naturally for large in spite of the theory being strongly coupled. The energy spectra on the two sides agree at leading order. This provides a non-trivial test of the AdS /CFT correspondence including near-BPS observables associated with membrane degrees of freedom, thus verifying the duality beyond the previously studied sectors corresponding to either BPS observables or the type IIA string regime

Large A t without the desert

Even if the unification and supersymmetry breaking scales are around 10 6 to 10 9 TeV, a large A t coupling may be entirely generated at low energies through RGE evolution in the 5D MSSM. Independent of the precise details of supersymmetry breaking, we take advantage of power law running in five dimensions and a compactification scale in the 10 − 10 3 TeV range to show how the gluino mass may drive a large enough A t to achieve the required 125 . 5 GeV Higgs mass. This also allows for sub-TeV stops, possibly observable at the LHC, and preserving GUT unification, thereby resulting in improved naturalness properties with respect to the four dimensional MSSM. The results apply also to models of “split families” in which the first and second generation matter fields are in the bulk and the third is on the boundary, which may assist in the generation of light stops whilst satisfying collider constraints on the first two generations of squarks

Physical states in the canonical tensor model from the perspective of random tensor networks

Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N = 2 , 3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N . Then, by generalizing this form, we also obtain various solutions for general N . Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N . This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N = 3, and comment on an extension of Airy function related to the solutions

Holography as a gauge phenomenon in Higher Spin duality

Employing the world line spinning particle picture. We discuss the appearance of several different ‘gauges’ which we use to gain a deeper explanation of the Collective/Gravity identification. We discuss transformations and algebraic equivalences between them. For a bulk identification we develop a ‘gauge independent’ representation where all gauge constraints are eliminated. This ‘gauge reduction’ of Higher Spin Gravity demonstrates that the physical content of 4D AdS HS theory is represented by the dynamics of an unconstrained scalar field in 6d. It is in this gauge reduced form that HS Theory can be seen to be equivalent to a 3 + 3 dimensional bi-local collective representation of CFT 3