scholarly journals Wilsonian Effective Action and Entanglement Entropy

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1221
Author(s):  
Satoshi Iso ◽  
Takato Mori ◽  
Katsuta Sakai
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Effective Action ◽  
Correlation Functions ◽  
Entanglement Entropy ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Non Gaussian

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of ZM gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.

scholarly journals RENORMALIZATION WITHOUT INFINITIES

2005 ◽  
Vol 20 (06) ◽  
pp. 1336-1345 ◽  
Author(s):  
GERARD 'T HOOFT
Keyword(s):  
Renormalization Group ◽  
Conceptual Understanding ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Renormalization Group Equations

Most renormalizable quantum field theories can be rephrased in terms of Feynman diagrams that only contain dressed irreducible 2-, 3-, and 4-point vertices. These irreducible vertices in turn can be solved from equations that also only contain dressed irreducible vertices. The diagrams and equations that one ends up with do not contain any ultraviolet divergences. The original bare Lagrangian of the theory only enters in terms of freely adjustable integration constants. It is explained how the procedure proposed here is related to the renormalization group equations. The procedure requires the identification of unambiguous "paths" in a Feynman diagrams, and it is shown how to define such paths in most of the quantum field theories that are in use today. We do not claim to have a more convenient calculational scheme here, but rather a scheme that allows for a better conceptual understanding of ultraviolet infinities.

scholarly journals Complementary projection defects and decomposition

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Fabian Klos ◽  
Daniel Roggenkamp
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Correlation Functions ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Topological Quantum ◽  
Renormalization Group Flows ◽  
Topological Quantum Field Theories

Abstract As put forward in [1] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An interesting example is the case of topological quantum field theories associated to IR fixed points of renormalization group flows, which by this method can be realized inside the theories associated to the UV. In this note we show that projection defects in triangulated defect categories (such as defects in 2d topologically twisted $$ \mathcal{N} $$ N = (2, 2) theories) always come with complementary projection defects, and that the unprojected theory decomposes into the theories associated to the two projection defects. We demonstrate this in the context of Landau-Ginzburg orbifold theories.

scholarly journals Entanglement entropy: non-Gaussian states and strong coupling

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
José J. Fernández-Melgarejo ◽  
Javier Molina-Vilaplana
Keyword(s):  
Ground State ◽  
Entanglement Entropy ◽  
Energy Functional ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Gaussian States ◽  
Strong Subadditivity ◽  
Point Correlation ◽  
Non Gaussian

Abstract In this work we provide a method to study the entanglement entropy for non-Gaussian states that minimize the energy functional of interacting quantum field theories at arbitrary coupling. To this end, we build a class of non-Gaussian variational trial wavefunctionals with the help of exact nonlinear canonical transformations. The calculability bonanza shown by these variational ansatze allows us to compute the entanglement entropy using the prescription for the ground state of free theories. In free theories, the entanglement entropy is determined by the two-point correlation functions. For the interacting case, we show that these two-point correlators can be replaced by their nonperturbatively corrected counterparts. Upon giving some general formulae for general interacting models we calculate the entanglement entropy of half space and compact regions for the ϕ4 scalar field theory in 2D. Finally, we analyze the rôle played by higher order correlators in our results and show that strong subadditivity is satisfied.

Estimates on Renormalization Group Transformations

1998 ◽  
Vol 50 (4) ◽  
pp. 756-793 ◽  
Author(s):  
D. Brydges ◽  
J. Dimock ◽  
T. R. Hurd
Keyword(s):  
Renormalization Group ◽  
Gaussian Measure ◽  
Ultra Violet ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
Scalar Quantum ◽  
Polymer Expansion ◽  
Renormalization Group Flows

AbstractWe consider a specific realization of the renormalization group (RG) transformation acting on functional measures for scalar quantum fields which are expressible as a polymer expansion times an ultra-violet cutoff Gaussian measure. The new and improved definitions and estimates we present are sufficiently general and powerful to allow iteration of the transformation, hence the analysis of complete renormalization group flows, and hence the construction of a variety of scalar quantum field theories.

scholarly journals On the renormalization of entanglement entropy

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Jin-Yi Pang ◽  
Jiunn-Wei Chen
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Scalar Field ◽  
Entanglement Entropy ◽  
Black Hole Entropy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Replica Trick ◽  
Dimensional Spacetime

AbstractThe renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a λϕ4 scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order λ once all the relevant operators up to dimension 4 are included in the action. This exercise has a one-to-one correspondence to entanglement entropy interpretation of the black hole entropy which suggests that our treatment is sensible. Our study suggests that entanglement entropy is renormalizable and is a physical quantity.

scholarly journals Frame covariant formalism for fermionic theories

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Kieran Finn ◽  
Sotirios Karamitsos ◽  
Apostolos Pilaftsis
Keyword(s):  
Effective Action ◽  
Degrees Of Freedom ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Covariant Formalism ◽  
Classical Action ◽  
Proper Definition ◽  
Definition Of ◽  
Standing Problem

AbstractWe present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky–DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem concerning the proper definition of a metric for fermionic theories. With the metric thus defined, we use well-established field-space techniques to extend the VDW effective action and express any fermionic theory in a frame- and field-reparametrisation-invariant manner.

scholarly journals Tensor Renormalization Group for interacting quantum fields

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 586
Author(s):  
Manuel Campos ◽  
German Sierra ◽  
Esperanza Lopez
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Real Space ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Excellent Performance ◽  
Tensor Network ◽  
Feynman Graphs

We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level of fields. This strategy was applied in Ref.[1] to the much simpler case of a free boson, obtaining an excellent performance. Here we include an arbitrary self-interaction and treat it in the context of perturbation theory. A real space analogue of the Wilsonian effective action and its expansion in Feynman graphs is proposed. Using a λϕ4 theory for benchmark, we evaluate the order λ correction to the free energy. The results show a fast convergence with the bond dimension, implying that our algorithm captures well the effect of interaction on entanglement.

NEW PERTURBATIVE APPROACH TO GENERAL RENORMALIZABLE QUANTUM FIELD THEORIES

1991 ◽  
Vol 06 (19) ◽  
pp. 3381-3397 ◽  
Author(s):  
V. GUPTA ◽  
D.V. SHIRKOV ◽  
O.V. TARASOV
Keyword(s):  
Renormalization Group ◽  
Perturbation Expansion ◽  
Renormalization Scheme ◽  
Coupling Constants ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Coupling Constant ◽  
Perturbative Approach ◽  
Coupling Case

We develop further the new approach to perturbation theory for renormalizable quantum field theories (proposed some years ago) which gives renormalization-scheme-independent predictions for observable quantities. We call the resulting REnormalization-Scheme-Independent PErturba-tion theory RESIPE, for short. First, we formulate explicitly the relation of RESIPE to the renormalization group formalism for the massless one-coupling case. Then we extend this to the case where particle masses cannot be neglected. Further, we generalize the RESIPE formalism for the theory with two coupling constants. A new scheme-invariant perturbation expansion, without reference to renormalization group techniques, is given which is valid for the general case with masses, several kinematic variables and more than one coupling constant. In conclusion, we argue that the appropriately generalized RESIPE provides us with a picture of perturbative predictions, for renormalizable quantum field theories, that is free from regularization and renormalization scheme ambiguities.

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