The 1/n expansion in the Gross-Neveu model: Conformal bootstrap calculation of the exponent 1/v to the order 1/n2

1993 ◽  
Vol 97 (3) ◽  
pp. 1349-1354 ◽  
Author(s):  
A. N. Vasil'ev ◽  
A. S. Stepanenko
Keyword(s):  
Bootstrap Calculation ◽  
Conformal Bootstrap ◽  
Gross Neveu Model

The 1/n expansion in the Gross-Neveu model: Conformal bootstrap calculation of the index ? in order 1/n 3

1993 ◽  
Vol 94 (2) ◽  
pp. 127-136 ◽  
Author(s):  
A. N. Vasil'ev ◽  
S. �. Derkachev ◽  
N. A. Kivel' ◽  
A. S. Stepanenko
Keyword(s):  
Bootstrap Calculation ◽  
Conformal Bootstrap ◽  
Gross Neveu Model

scholarly journals COMPUTATION OF CRITICAL EXPONENT η AT O(1/N3) IN THE FOUR-FERMI MODEL IN ARBITRARY DIMENSIONS

1994 ◽  
Vol 09 (05) ◽  
pp. 727-744 ◽  
Author(s):  
J.A. GRACEY
Keyword(s):  
Critical Exponent ◽  
Anomalous Dimension ◽  
Fermi Model ◽  
Conformal Bootstrap ◽  
Arbitrary Dimensions ◽  
Gross Neveu Model

We solve the conformal bootstrap equations of the four-fermi model or O(N) Gross-Neveu model to deduce the fermion anomalous dimension of the theory at O(1/N3) in arbitrary dimensions.

scholarly journals Loops in AdS: from the spectral representation to position space. Part II

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dean Carmi
Keyword(s):  
Spectral Representation ◽  
Tree Level ◽  
Point Function ◽  
Position Space ◽  
Gross Neveu Model ◽  
Loop Amplitudes

Abstract We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-N conformal Gross Neveu model on AdS3. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].

scholarly journals Bootstrap bounds on closed Einstein manifolds

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
James Bonifacio ◽  
Kurt Hinterbichler
Keyword(s):  
Compact Riemannian Manifold ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Einstein Manifolds ◽  
Consistency Conditions ◽  
Conformal Field ◽  
Geometric Data ◽  
Conformal Bootstrap ◽  
Laplacian Operators ◽  
Kaluza Klein

Abstract A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

scholarly journals The Gross-Neveu model at finite temperature and density

1987 ◽  
Vol 280 ◽  
pp. 289-303 ◽  
Author(s):  
F. Karsch ◽  
J. Kogut ◽  
H.W. Wyld
Keyword(s):  
Finite Temperature ◽  
Gross Neveu Model
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