scholarly journals Towards a double scaling limit for tensor models: probing sub-dominant orders

2014 ◽  
Vol 16 (6) ◽  
pp. 063048 ◽  
Author(s):  
Wojciech Kamiński ◽  
Daniele Oriti ◽  
James P Ryan
Keyword(s):  
Scaling Limit ◽  
Tensor Models ◽  
Double Scaling Limit

Random tensor models—the U(N)D-invariant model

2021 ◽  
pp. 178-208
Author(s):  
Adrian Tanasa
Keyword(s):  
Scaling Limit ◽  
Point Function ◽  
Invariant Model ◽  
Invariant Tensor ◽  
The Third ◽  
Tensor Models ◽  
Random Tensor ◽  
Combinatorial Methods ◽  
Double Scaling Limit ◽  
The Way

In the first section we give a briefly presentation of the U(N)D-invariant tensor models (N being again the size of the tensor, and D being the dimension). The next section is then dedicated to the analysis of the Dyson–Schwinger equations (DSE) in the large N limit. These results are essential to implement the double scaling limit mechanism of the DSEs, which is done in the third section. The main result of this chapter is the doubly-scaled 2-point function for a model with generic melonic interactions. However, several assumptions on the large N scaling of cumulants are made along the way. They are proved using various combinatorial methods.

scholarly journals Double scaling limit for the O(N)3-invariant tensor model

2022 ◽  
Author(s):  
Valentin Bonzom ◽  
Victor Nador ◽  
Adrian Tanasa
Keyword(s):  
Scaling Limit ◽  
Tensor Model ◽  
Invariant Tensor ◽  
Generating Series ◽  
Tensor Models ◽  
Feynman Graphs ◽  
Diagrammatic Analysis ◽  
Finite Sum ◽  
Double Scaling Limit ◽  
The Continuum

Abstract We study the double scaling limit of the O(N)3-invariant tensor model, initially introduced in Carrozza and Tanasa, Lett. Math. Phys. (2016). This model has an interacting part containing two types of quartic invariants, the tetrahedric and the pillow one. For the 2-point function, we rewrite the sum over Feynman graphs at each order in the 1/N expansion as a finite sum, where the summand is a function of the generating series of melons and chains (a.k.a. ladders). The graphs which are the most singular in the continuum limit are characterized at each order in the 1/N expansion. This leads to a double scaling limit which picks up contributions from all orders in the 1/N expansion. In contrast with matrix models, but similarly to previous double scaling limits in tensor models, this double scaling limit is summable. The tools used in order to prove our results are combinatorial, namely a thorough diagrammatic analysis of the Feynman graphs, as well as an analytic analysis of the singularities of the relevant generating series.

scholarly journals The double scaling limit of random tensor models

2014 ◽  
Vol 2014 (9) ◽  
Author(s):  
Valentin Bonzom ◽  
Razvan Gurau ◽  
James P. Ryan ◽  
Adrian Tanasa
Keyword(s):  
Scaling Limit ◽  
Tensor Models ◽  
Random Tensor ◽  
Double Scaling Limit

scholarly journals Characters of irrelevant deformations

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Shouvik Datta ◽  
Yunfeng Jiang
Keyword(s):  
Deformation Parameter ◽  
Central Charge ◽  
Scaling Limit ◽  
Small Deformation ◽  
State Dependent ◽  
Dependent Change ◽  
Left And Right ◽  
Double Scaling Limit

Abstract We analyse the $$ T\overline{T} $$ T T ¯ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve $$ T\overline{T} $$ T T ¯ , $$ J\overline{T} $$ J T ¯ and $$ T\overline{J} $$ T J ¯ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

scholarly journals THE CRITICAL POINT OF UNORIENTED RANDOM SURFACES WITH A NONEVEN POTENTIAL

1993 ◽  
Vol 08 (06) ◽  
pp. 1139-1152
Author(s):  
M.A. MARTÍN-DELGADO
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Critical Point ◽  
Discrete Model ◽  
Recursion Relation ◽  
Scaling Limit ◽  
Random Surfaces ◽  
Matrix Ensemble ◽  
Quartic Interaction ◽  
Double Scaling Limit

The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double scaling-limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a quartic interaction.

scholarly journals Hexagon bootstrap in the double scaling limit

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Vsevolod Chestnov ◽  
Georgios Papathanasiou
Keyword(s):  
Function Space ◽  
Operator Product Expansion ◽  
General Pattern ◽  
Scaling Limit ◽  
Kinematic Region ◽  
Operator Product ◽  
Yang Mills ◽  
Codimension One ◽  
Double Scaling Limit ◽  
Super Yang Mills Theory

Abstract We study the six-particle amplitude in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory in the double scaling (DS) limit, the only nontrivial codimension-one boundary of its positive kinematic region. We construct the relevant function space, which is significantly constrained due to the extended Steinmann relations, up to weight 13 in coproduct form, and up to weight 12 as an explicit polylogarithmic representation. Expanding the latter in the collinear boundary of the DS limit, and using the Pentagon Operator Product Expansion, we compute the non-divergent coefficient of a certain component of the Next-to-Maximally-Helicity-Violating amplitude through weight 12 and eight loops. We also specialize our results to the overlapping origin limit, observing a general pattern for its leading divergences.

scholarly journals NON-PERTURBATIVE SOLUTION OF THE SUPER-VIRASORO CONSTRAINTS

1993 ◽  
Vol 08 (13) ◽  
pp. 1205-1214 ◽  
Author(s):  
K. BECKER ◽  
M. BECKER
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Scaling Limit ◽  
Virasoro Constraints ◽  
Perturbative Solution ◽  
The One ◽  
Genus Expansion ◽  
Double Scaling Limit

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the non-perturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.

scholarly journals ON THE CONTINUUM LIMIT OF THE CONFORMAL MATRIX MODELS

1993 ◽  
Vol 08 (18) ◽  
pp. 3107-3137 ◽  
Author(s):  
A. MIRONOV ◽  
S. PAKULIAK
Keyword(s):  
Matrix Models ◽  
Continuum Limit ◽  
Scaling Limit ◽  
Universality Class ◽  
Partition Functions ◽  
Discrete Level ◽  
New Class ◽  
Double Scaling Limit ◽  
The Continuum

The double scaling limit of a new class of the multi-matrix models proposed in Ref. 1, which possess the W-symmetry at the discrete level, is investigated in detail. These models are demonstrated to fall into the same universality class as the standard multi-matrix models. In particular, the transformation of the W-algebra at the discrete level into the continuum one of the papers2 is proposed and the corresponding partition functions compared. All calculations are demonstrated in full in the first nontrivial case of W(3)-constraints.

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