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arXiv:1505.00586 · Europhysics Letters (EPL)

The double scaling limit of the multi-orientable tensor model

Razvan Gurău, Adrian Tanasă, Donald R. Youmans

Published Jul 1, 2015• 52 citations
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Abstract

In this paper we study the double scaling limit of the multi-orientable tensor model. We prove that, contrary to the case of matrix models but similarly to the case of invariant tensor models, the double scaling series are convergent. We resum the double scaling series of the two-point function and of the leading singular part of the four-point function. We discuss the behavior of the leading singular part of arbitrary correlation functions. We show that the contribution of the four-point function and of all the higher point functions are enhanced in the double scaling limit. We finally show that all the correlation functions exhibit a singularity at the same critical value of the double scaling parameter which, combined with the convergence of the double scaling series, suggest the existence of a triple scaling limit.

DOI
10.1209/0295-5075/111/21002

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Abstract This chapter presents the double scaling limit of quartic tensor models. In the first part of this chapter it is shown show that the melonic family in the quartic melonic tensor model can be analytically resumed and that this resummation is encoded in a translation of the intermediate matrix fields to a nontrivial vacuum. The most striking consequence of this translation is that one can now show that the continuum limit of tensor models corresponds to a genuine phase transition (in the field theory sense) associated to a symmetry breaking. In the second part of this chapter the intermediate field representation is used to derive the double scaling limit of the quartic melonic model.
The definition of a double-scaling limit represents an important goal in the development of tensor models.We take the first steps towards this goal by extracting and analysing the next-to-leading order contributions, in the 1/N expansion, for the iid tensor models.We show that the radius of convergence of the nlo series coincides with that of the leading order melonic sector.Meanwhile, the value of the susceptibility exponent, γnlo = 3/2, signals a departure from the leading order behaviour.Both pieces of information provide clues for a non-trivial double-scaling limit, for which we put forward some precise conjecture.
Abstract In Giombi et al (2018 Phys. Rev. D 98 105005), a prismatic tensor model was introduced. We study here the diagrammatics and the double scaling limit of this model, using the intermediate field method. We explicitly exhibit the next-to-leading order Feynman graphs in the 1 / N expansion. Using appropriate combinatorial tools, we further study the general term of the 1 / N expansion and we compute the two-point function in the double scaling limit. We find that the double scaling limit mechanism implemented here is similar to the one implemented for various quartic tensor models.
Entanglement scaling for λϕ24λϕ_2^4λϕ24​
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A detailed calculation to order ${\ensuremath{\epsilon}}^{2}$ of the two-point correlation function in the zero-field critical region ($T\ensuremath{\ge}{T}_{c}$) is presented for an nnn-vector system in $d=4\ensuremath{-}\ensuremath{\epsilon}$ dimensions. Scaling behavior is verified over the full parameter range and the scaling function is obtained as a universal explicit convergent integral (independent of any cutoffs). Study of the scaling function as $T\ensuremath{\rightarrow}{T}_{c}$ in the finite ($q\ensuremath{\ne}0$) momentum limit, confirms the presence of terms varying as ${t}^{1\ensuremath{-}\ensuremath{\alpha}}$ and as ttt [with $t=\frac{(T\ensuremath{-}{T}_{c})}{{T}_{c}}$]; explicit evaluation of their amplitudes reliably determines the form of the scattering intensity at fixed qqq and locates the corresponding maximum accurately.