2,588 research outputs found

### 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 the generalization of the previous one
concerning the relation between the Ising model on random networks and the
canonical tensor model with N=2. We also prove a general theorem which relates
discontinuity of the renormalization-group flow and the phase transitions of
random tensor networks.Comment: 23 pages, 5 figures; Comments on first order transitions and
discontinuity of RG added, and minor correction

### 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
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.Comment: 9 page

### 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.Comment: 41 pages, 1 figure; typos correcte

### On membrane interactions and a three-dimensional analog of Riemann surfaces

Membranes in M-theory are expected to interact via splitting and joining
processes. We study these effects in the pp-wave matrix model, in which they
are associated with transitions between states in sectors built on vacua with
different numbers of membranes. Transition amplitudes between such states
receive contributions from BPS instanton configurations interpolating between
the different vacua. Various properties of the moduli space of BPS instantons
are known, but there are very few known examples of explicit solutions. We
present a new approach to the construction of instanton solutions interpolating
between states containing arbitrary numbers of membranes, based on a continuum
approximation valid for matrices of large size. The proposed scheme uses
functions on a two-dimensional space to approximate matrices and it relies on
the same ideas behind the matrix regularisation of membrane degrees of freedom
in M-theory. We show that the BPS instanton equations have a continuum
counterpart which can be mapped to the three-dimensional Laplace equation
through a sequence of changes of variables. A description of configurations
corresponding to membrane splitting/joining processes can be given in terms of
solutions to the Laplace equation in a three-dimensional analog of a Riemann
surface, consisting of multiple copies of R^3 connected via a generalisation of
branch cuts. We discuss various general features of our proposal and we also
present explicit analytic solutions.Comment: 64 pages, 17 figures. V2: An appendix, a figure and references added;
various minor changes and improvement

### Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS_4/CFT_3

We consider states with large angular momentum to facilitate the study of the
M-theory regime of the AdS_4/CFT_3 correspondence. We study the duality between
M-theory in AdS_4xS^7/Z_k and the ABJM N=6 Chern-Simons-matter theory with
gauge group U(N)xU(N) and level k, taking N large and k of order 1. In this
regime the lack of an explicit formulation of M-theory in AdS_4xS^7/Z_k makes
the gravity side difficult, while the CFT is strongly coupled and the planar
approximation is not applicable. To overcome these difficulties, we focus on
states on the gravity side with large angular momentum J>>1 and identify the
dual operators in the CFT, thereby establishing the AdS/CFT dictionary in this
sector. Natural approximation schemes arise on both sides thanks to the
presence of the small parameter 1/J. On the AdS side, we use the matrix model
of M-theory on the maximally supersymmetric pp-wave background with matrices of
size J/k. A perturbative treatment of this matrix model provides a good
approximation to M-theory in AdS_4xS^7/Z_k when N^{1/3}<<J<<N^{1/2}. On the CFT
side, we study the theory on S^2xR with magnetic flux J/k. A Born-Oppenheimer
type expansion arises naturally for large J 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_4/CFT_3 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.Comment: 67 pages, 5 figures; V2: minor changes, references adde

### n-DBI gravity

n-DBI gravity is a gravitational theory introduced in arXiv:1109.1468
[hep-th], motivated by Dirac-Born-Infeld type conformal scalar theory and
designed to yield non-eternal inflation spontaneously. It contains a foliation
structure provided by an everywhere time-like vector field n, which couples to
the gravitational sector of the theory, but decouples in the small curvature
limit. We show that any solution of Einstein gravity with a particular
curvature property is a solution of n-DBI gravity. Amongst them is a class of
geometries isometric to Reissner-Nordstrom-(Anti) de Sitter black hole, which
is obtained within the spherically symmetric solutions of n-DBI gravity
minimally coupled to the Maxwell field. These solutions have, however, two
distinct features from their Einstein gravity counterparts: 1) the cosmological
constant appears as an integration constant and can be positive, negative or
vanishing, making it a variable quantity of the theory; 2) there is a
non-uniqueness of solutions with the same total mass, charge and effective
cosmological constant. Such inequivalent solutions cannot be mapped to each
other by a foliation preserving diffeomorphism. Physically they are
distinguished by the expansion and shear of the congruence tangent to n, which
define scalar invariants on each leave of the foliation.Comment: 13 page

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