Truncated Hilbert Space Approach

2020 ◽  
pp. 943-974
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Hilbert Space ◽  
Conformal Field Theory ◽  
Finite Geometry ◽  
Infinite Cylinder ◽  
Conformal Field ◽  
Scaling Region ◽  
Critical Model ◽  
The Masses ◽  
Space Approach

Chapter 25 covers the Truncated Hilbert Space Approach provides a very efficient numerical algorithm to study many properties of a perturbed conformal field theory defined on a finite geometry, typically an infinite cylinder of radius R. These include the masses of the various excitations, their number below threshold, the presence of false vacua and resonances, on-shell three-particle coupling, etc. The implementation of this approach does not depend on the integrability of the off-critical model and therefore it is a very useful tool to extend study to the entire scaling region around the critical point. This chapter discusses the basis of such an algorithm and provides some interesting applications thereof.

scholarly journals FERMIONIC SUBSPACES OF THE BOSONIC STRING

2004 ◽  
Vol 19 (supp02) ◽  
pp. 117-125
Author(s):  
A. CHATTARAPUTI ◽  
F. ENGLERT ◽  
L. HOUART ◽  
A. TAORMINA
Keyword(s):  
Field Theory ◽  
Hilbert Space ◽  
Group Theory ◽  
Conformal Field Theory ◽  
Crucial Role ◽  
Predictive Power ◽  
Bosonic String ◽  
Two Dimensional ◽  
Conformal Field ◽  
Fermionic String

A universal symmetric truncation of the bosonic string Hilbert space yields all known closed fermionic string theories in ten dimensions, their D-branes and their open descendants. We highlight the crucial role played by group theory and two-dimensional conformal field theory in the construction and emphasize the predictive power of the truncation. Such circumstantial evidence points towards the existence of a mechanism which generates space-time fermions out of bosons dynamically within the framework of bosonic string theory.

scholarly journals Holographic entanglement entropy for noncommutative anti-de Sitter space

2016 ◽  
Vol 31 (12) ◽  
pp. 1650073
Author(s):  
Davood Momeni ◽  
Muhammad Raza ◽  
Ratbay Myrzakulov
Keyword(s):  
Field Theory ◽  
Hilbert Space ◽  
Conformal Field Theory ◽  
Surface State ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Quantum Effects ◽  
De Sitter ◽  
Conformal Field ◽  
Holographic Entanglement Entropy

A metric is proposed to explore the noncommutative form of the anti-de Sitter (AdS) space due to quantum effects. It has been proved that the noncommutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu–Takayanagi (RT) algorithm is then applied to compute the entanglement entropy (EE) in dual CFT2. This calculation can be exploited to compute ultraviolet–infrared (UV–IR) cutoff dependent central charge of the certain noncommutative CFT2. This noncommutative computation of the EE can be interpreted in the form of the surface/state correspondence. We have shown that noncommutativity increases the dimension of the effective Hilbert space of the dual conformal field theory (CFT).

The physical states of a boundary conformal field theory

2020 ◽  
Vol 35 (06) ◽  
pp. 2050021
Author(s):  
Simon Davis
Keyword(s):  
Field Theory ◽  
Hilbert Space ◽  
Conformal Field Theory ◽  
Vacuum State ◽  
Linear Measure ◽  
Ideal Boundary ◽  
Residue Theorem ◽  
Conformal Field ◽  
Nonperturbative Effect ◽  
The Ideal

The path integral of a conformal field theory on a bordered Riemann surface defines a state in a Hilbert space on this boundary. Over the ideal boundary, the Hausdorff dimension may be less than one. The integral representing the flux over the ideal boundary is evaluated through a generalization of the residue theorem. The identification of the state for infinite-genus surfaces with the vacuum state with a perturbative vacuum is distinguished from the Hilbert space on ideal boundaries of nonzero linear measure. This nonperturbative effect is identified as an instanton in a separate quantum theory.

TRUNCATED COMFORMAL SPACE APPROACH TO SCALING LEE-YANG MODEL

1990 ◽  
Vol 05 (16) ◽  
pp. 3221-3245 ◽  
Author(s):  
V. P. YUROV ◽  
AL. B. ZAMOLODCHIKOV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Numerical Approach ◽  
Theory Model ◽  
Ultraviolet Region ◽  
Conformal Theory ◽  
Conformal Field ◽  
Finite Dimensional ◽  
Theory Formula ◽  
Space Approach

A numerical approach to 2-D relativistic field theories is suggested. Considering a field theory model as an ultraviolet conformal field theory perturbed by a suitable relevant scalar operator one studies it in finite volume (on a circle). The perturbed Hamiltonian acts in the conformal field theory space of states and its matrix elements can be extracted from the conformal field theory. Truncation of the space at a reasonable level results in a finite dimensional problem for numerical analyses. The nonunitary field theory with the ultraviolet region controlled by the minimal conformal theory [Formula: see text] is studied in detail.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

scholarly journals THE FREE FIELD REPRESENTATION OF SU(3) CONFORMAL FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Free Field ◽  
Field Representation ◽  
Conformal Field ◽  
Point Correlation

The structure of the free field representation and some four-point correlation functions of the SU(3) conformal field theory are considered.

scholarly journals Decoherence in Conformal Field Theory

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Adolfo del Campo ◽  
Tadashi Takayanagi
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Field

scholarly journals Parafermionization, bosonization, and critical parafermionic theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yuan Yao ◽  
Akira Furusaki
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Degrees Of Freedom ◽  
Lattice Models ◽  
Partition Functions ◽  
Minimal Models ◽  
Fermionic Model ◽  
Conformal Field ◽  
Critical Theories ◽  
Wigner Transformation

AbstractWe formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

Sign in / Sign up

Export Citation Format

Share Document