scholarly journals T $$ \overline{T} $$-flow effects on torus partition functions

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Song He ◽  
Yuan Sun ◽  
Yu-Xuan Zhang
Keyword(s):  
Hamiltonian Formalism ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Partition Functions ◽  
Majorana Fermions ◽  
Dirac Fermions ◽  
Conformal Field Theories ◽  
First Order ◽  
Conformal Field ◽  
Flow Effects

Abstract In this paper, we investigate the partition functions of conformal field theories (CFTs) with the T$$ \overline{T} $$ T ¯ deformation on a torus in terms of the perturbative QFT approach. In Lagrangian path integral formalism, the first- and second-order deformations to the partition functions of 2D free bosons, free Dirac fermions, and free Majorana fermions on a torus are obtained. The corresponding Lagrangian counterterms in these theories are also discussed. The first two orders of the deformed partition functions and the first-order vacuum expectation value (VEV) of the first quantum KdV charge obtained by the perturbative QFT approach are consistent with results obtained by the Hamiltonian formalism in literature.

scholarly journals A nilpotency index of conformal manifolds

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Zohar Komargodski ◽  
Shlomo S. Razamat ◽  
Orr Sela ◽  
Adar Sharon
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Generic Point ◽  
Expectation Value ◽  
Conformal Field ◽  
Chiral Ring ◽  
Nilpotency Index ◽  
Conformal Manifolds

Abstract We show that exactly marginal operators of Supersymmetric Conformal Field Theories (SCFTs) with four supercharges cannot obtain a vacuum expectation value at a generic point on the conformal manifold. Exactly marginal operators are therefore nilpotent in the chiral ring. This allows us to associate an integer to the conformal manifold, which we call the nilpotency index of the conformal manifold. We discuss several examples in diverse dimensions where we demonstrate these facts and compute the nilpotency index.

Conformal Field Theory of Free Bosonic and Fermionic Fields

2020 ◽  
pp. 443-475
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theories ◽  
Majorana Fermion ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Bosonic Field ◽  
Conformal Field ◽  
Mathematical Identities ◽  
Modular Transformations ◽  
Fermionic Fields ◽  
The Subject

Free theories are usually regarded as trivial examples of quantum systems. This chapter proves that this is not the case of the conformal field theories associated to the free bosonic and fermionic fields. The subject is not only full of beautiful mathematical identities but is also the source of deep physical concepts with far reaching applications. Chapter 12 also covers quantization of the bosonic field, vertex operators, the free bosonic field on a torus, modular transformations, the quantization of the free Majorana fermion, the Neveu–Schwarz and Ramond sectors, fermions on a torus, calculus for anti-commuting quantities and partition functions.

scholarly journals BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY

2003 ◽  
Vol 18 (25) ◽  
pp. 4497-4591 ◽  
Author(s):  
MICHAEL A. I. FLOHR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Hall ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory ◽  
Verlinde Formula

These are notes of my lectures held at the first School & Workshop on Logarithmic Conformal Field Theory and its Applications, September 2001 in Tehran, Iran. These notes cover only selected parts of the by now quite extensive knowledge on logarithmic conformal field theories. In particular, I discuss the proper generalization of null vectors towards the logarithmic case, and how these can be used to compute correlation functions. My other main topic is modular invariance, where I discuss the problem of the generalization of characters in the case of indecomposable representations, a proposal for a Verlinde formula for fusion rules and identities relating the partition functions of logarithmic conformal field theories to such of well known ordinary conformal field theories. The two main topics are complemented by some remarks on ghost systems, the Haldane-Rezayi fractional quantum Hall state, and the relation of these two to the logarithmic c=-2 theory.

scholarly journals TOWERS OF ALGEBRAS IN RATIONAL CONFORMAL FIELD THEORIES

1991 ◽  
Vol 06 (12) ◽  
pp. 2045-2074 ◽  
Author(s):  
CÉSAR GOMEZ ◽  
GERMAN SIERRA
Keyword(s):  
Sufficient Conditions ◽  
Field Theories ◽  
Partition Functions ◽  
Polynomial Equations ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Ade Classification

Jones fundamental construction is applied to rational conformal field theories. The Jones algebra which emerges in this application is realized in terms of duality operations. The generators of the algebra are an open version of Verlinde’s operators. The polynomial equations appear in this context as sufficient conditions for the existence of Jones algebra. The ADE classification of modular invariant partition functions is put in correspondence with Jones classification of subfactors.

scholarly journals CLONING SO(N) LEVEL 2

1999 ◽  
Vol 14 (08) ◽  
pp. 1283-1291 ◽  
Author(s):  
A. N. SCHELLEKENS
Keyword(s):  
Infinite Number ◽  
Essential Role ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Chiral Algebra ◽  
Conformal Field ◽  
N Level ◽  
Level 2

For each N an infinite number of conformal field theories is presented that has the same fusion rules as SO (N) level 2. These new theories are obtained as extensions of the chiral algebra of SO (NM2) level 2, and correspond to new modular invariant partition functions of these theories. A one-to-one map between the c=1 orbifolds of radius R2=2r and Dr level 2 plays an essential role.

CONFORMAL FIELD THEORIES ON SURFACES WITH BOUNDARIES AND CROSSCAPS

1989 ◽  
Vol 04 (02) ◽  
pp. 161-168 ◽  
Author(s):  
TETSUYA ONOGI ◽  
NOBUYUKI ISHIBASHI
Keyword(s):  
Crucial Role ◽  
Model Building ◽  
Open String ◽  
Theory Model ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Loop Channel

We classify the possible operator contents of the minimal conformal field theories when boundaries and crosscaps are present by imposing loop channel-tree channel duality conditions. These are the open string analogues of modular invariant partition functions, which play a crucial role in string theory model building.

scholarly journals Electroweak Phase Transitions in Einstein’s Static Universe

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
M. Gogberashvili
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Electroweak Phase Transition ◽  
Static Universe ◽  
Expectation Value ◽  
First Order ◽  
Higgs Vacuum ◽  
The Standard Model ◽  
Effective Reduction ◽  
New Phase

We suggest using Einstein’s static universe metric for the metastable state after reheating, instead of the Friedman-Robertson-Walker spacetime. In this case, strong static gravitational potential leads to the effective reduction of the Higgs vacuum expectation value, which is found to be compatible with the Standard Model first-order electroweak phase transition conditions. Gravity could also increase the CP-violating effects for particles that cross the new phase bubble walls and thus is able to lead to the successful electroweak baryogenesis scenario.

scholarly journals THE CAPPELLI–ITZYKSON–ZUBER A-D-E CLASSIFICATION

2000 ◽  
Vol 12 (05) ◽  
pp. 739-748 ◽  
Author(s):  
TERRY GANNON
Keyword(s):  
Mathematical Structure ◽  
The Other ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Affine Algebras ◽  
Order Of Magnitude ◽  
The Rich

In 1986 Cappelli, Itzykson and Zuber classified all modular invariant partition functions for the conformal field theories associated to the affine A1 algebra; they found they fall into an A-D-E pattern. Their proof was difficult and attempts to generalise it to the other affine algebras failed — in hindsight the reason is that their argument ignored most of the rich mathematical structure present. We give here the "modern" proof of their result; it is an order of magnitude simpler and shorter, and much of it has already been extended to all other affine algebras. We conclude with some remarks on the A-D-E pattern appearing in this and other RCFT classifications.

LOCALIZED MODES IN SINGULAR CALABI-YAU CONFORMAL FIELD THEORIES

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2184-2186
Author(s):  
SHUN'YA MIZOGUCHI
Keyword(s):  
Discrete Series ◽  
Field Theories ◽  
Partition Functions ◽  
Type Ii ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Heterotic Strings ◽  
Conformal Field ◽  
Series Representations ◽  
Discrete Series Representations

We construct spacetime supersymmetric, modular invariant partition functions for type II and heterotic strings on the conifold-type singularities such that they include contributions coming from the discrete-series representations of SL(2, R). In particular for the E8 × E8 heterotic case, they are in the 27 representation of E6 and localized on a four-dimensional "brane" at the tip of the cigar geometry.

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