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Spectrum of Majorana Quantum Mechanics with <math><mrow><mi>O</mi><mo>(</mo><mn>4</mn><msup><mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow></math> Symmetry
https://repo.scoap3.org/record/30224
We study the quantum mechanics of three-index Majorana fermions ψabc governed by a quartic Hamiltonian with O(N)3 symmetry. Similarly to the Sachdev-Ye-Kitaev model, this tensor model has a solvable large-N limit dominated by the melonic diagrams. For N=4 the total number of states is 232, but they naturally break up into distinct sectors according to the charges under the U(1)×U(1) Cartan subgroup of one of the O(4) groups. The biggest sector has vanishing charges and contains over 165 million states. Using a Lanczos algorithm, we determine the spectrum of the low-lying states in this and other sectors. We find that the absolute ground state is nondegenerate. If the SO(4)3 symmetry is gauged, it is known from earlier work that the model has 36 states and a residual discrete symmetry. We study the discrete symmetry group in detail; it gives rise to degeneracies of some of the gauge singlet energies. We find all the gauge singlet energies numerically and use the results to propose exact analytic expressions for them.Pakrouski, KirylFri, 11 Jan 2019 15:17:58 GMThttps://repo.scoap3.org/record/30224urn:ISSN:1079-7114APS2019-01-10Prismatic large <math><mi>N</mi></math> models for bosonic tensors
https://repo.scoap3.org/record/29166
We study the O(N)3 symmetric quantum field theory of a bosonic tensor ϕabc with sextic interactions. Its large N limit is dominated by a positive-definite operator, whose index structure has the topology of a prism. We present a large N solution of the model using Schwinger-Dyson equations to sum the leading diagrams, finding that for 2.81<d<3 and for d<1.68 the spectrum of bilinear operators has no complex scaling dimensions. We also develop perturbation theory in 3−ε dimensions including eight O(N)3 invariant operators necessary for the renormalizability. For sufficiently large N, we find a “prismatic” fixed point of the renormalization group, where all eight coupling constants are real. The large N limit of the resulting ε expansions of various operator dimensions agrees with the Schwinger-Dyson equations. Furthermore, the ε expansion allows us to calculate the 1/N corrections to operator dimensions. The prismatic fixed point in 3−ε dimensions survives down to N≈53.65, where it merges with another fixed point and becomes complex. We also discuss the d=1 model where our approach gives a slightly negative scaling dimension for ϕ, while the spectrum of bilinear operators is free of complex dimensions.Giombi, SimoneWed, 14 Nov 2018 17:16:47 GMThttps://repo.scoap3.org/record/29166urn:ISSN:2470-0029APS2018-11-14Debye mass in de Sitter space
https://repo.scoap3.org/record/26035
We calculate the one-loop contributions to the polarization operator for scalar quantum electrodynamics in different external electromagnetic and gravitational fields. In the case of gravity, de Sitter space and its different patches were considered. It is shown that the Debye mass appears only in the case of alpha-vacuum in the Expanding Poincare Patch. It can be shown either by direct computations or by using analytical and causal properties of the de Sitter space. Also, the case of constant electric field is considered and the Debye mass is calculated.Popov, FedorThu, 07 Jun 2018 08:19:25 GMThttps://repo.scoap3.org/record/26035urn:ISSN:1029-8479Springer/SISSA2018-06-06Spectra of eigenstates in fermionic tensor quantum mechanics
https://repo.scoap3.org/record/25915
We study the O(N1)×O(N2)×O(N3) symmetric quantum mechanics of 3-index Majorana fermions. When the ranks Ni are all equal, this model has a large N limit which is dominated by the melonic Feynman diagrams. We derive an integral formula which computes the number of group invariant states for any set of Ni. It is non-vanishing only when each Ni is even. For equal ranks the number of singlets exhibits rapid growth with N: it jumps from 36 in the O(4)3 model to 595 354 780 in the O(6)3 model. We derive bounds on the values of energy, which show that they scale at most as N3 in the large N limit, in agreement with expectations. We also show that the splitting between the lowest singlet and non-singlet states is of order 1/N. For N3=1 the tensor model reduces to O(N1)×O(N2) fermionic matrix quantum mechanics, and we find a simple expression for the Hamiltonian in terms of the quadratic Casimir operators of the symmetry group. A similar expression is derived for the complex matrix model with SU(N1)×SU(N2)×U(1) symmetry. Finally, we study the N3=2 case of the tensor model, which gives a more intricate complex matrix model whose symmetry is only O(N1)×O(N2)×U(1). All energies are again integers in appropriate units, and we derive a concise formula for the spectrum. The fermionic matrix models we studied possess standard ’t Hooft large N limits where the ground state energies are of order N2, while the energy gaps are of order 1.Klebanov, Igor R.Thu, 31 May 2018 20:16:06 GMThttps://repo.scoap3.org/record/25915urn:ISSN:2470-0029APS2018-05-31Ultraviolet phenomena in AdS self-interacting quantum field theory
https://repo.scoap3.org/record/24677
We study the one-loop corrections to the four-point function in the Anti de Sitter space-time for a ϕ 4 field theory. Our calculation shows the existence of non-local counterterms which however respect the AdS isometry. Our arguments are quite general and applicable to other AdS field theories. We also explain why calculations in Euclidean and Lorentzian signatures should differ even at the leading order in non globaly hyperbolic manifolds.Akhmedov, EmilFri, 30 Mar 2018 10:32:59 GMThttps://repo.scoap3.org/record/24677urn:ISSN:1029-8479Springer/SISSA2018-03-29