Mass generation in the large N Gross-Neveu model: a constructive proof without intermediate field

2021 ◽  
Author(s):  
Jeremie M. Unterberger
Keyword(s):  
Discrete Symmetry ◽  
Two Dimensions ◽  
Constructive Proof ◽  
Point Function ◽  
Large Component ◽  
Mass Generation ◽  
Bosonic Field ◽  
Large N ◽  
Discrete Symmetry Breaking ◽  
Gross Neveu Model

Abstract We give a new constructive proof of the infrared behavior of the Euclidean Gross-Neveu model in two dimensions with small coupling and large component number N. Our argument does not rely on the use of an intermediate (auxiliary bosonic) field. Instead bubble series are resummed by hand, and determinant bounds replaced by a control of local factorials relying on combinatorial arguments and Pauli's principle. The discrete symmetry-breaking is ensured by considering the model directly with a mass counterterm chosen in such a way as to cancel tadpole diagrams. Then the fermion two-point function is shown to decay (quasi-)exponentially as in [12]/

scholarly journals Mass generation in the large N Gross-Neveu-Model

1995 ◽  
Vol 169 (1) ◽  
pp. 121-180 ◽  
Author(s):  
C. Kopper ◽  
J. Magnen ◽  
V. Rivasseau
Keyword(s):  
Mass Generation ◽  
Large N ◽  
Gross Neveu Model

scholarly journals STRING HAMILTONIAN FROM GENERALIZED YANG–MILLS GAUGE THEORY IN TWO DIMENSIONS

2004 ◽  
Vol 19 (02) ◽  
pp. 205-225 ◽  
Author(s):  
FLORIAN DUBATH ◽  
SIMONE LELLI ◽  
ANNA RISSONE
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Space Time ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Bosonic Field ◽  
Standard Case ◽  
Free Fermions ◽  
Yang Mills ◽  
Large N

Two-dimensional SU (N) Yang–Mills theory is known to be equivalent to a string theory, as found by Gross in the large N limit, using the 1/N expansion. Later it was found that even a generalized YM theory leads to a string theory of the Gross type. In the standard YM theory case, Douglas and others found the string Hamiltonian describing the propagation and the interactions of states made of strings winding on a cylindrical space–time. We address the problem of finding a similar Hamiltonian for the generalized YM theory. As in the standard case we start by writing the theory as a theory of free fermions. Performing a bosonization, we express the Hamiltonian in terms of the modes of a bosonic field, that are interpreted as in the standard case as creation and destruction operators for states of strings winding around the cylindrical space–time. The result is similar to the standard Hamiltonian, but with new kinds of interaction vertices.

scholarly journals The 2D Gross–Neveu model for pseudovector fermions and tachyonic mass generation

2015 ◽  
Vol 12 (09) ◽  
pp. 1550090
Author(s):  
V. K. Oikonomou
Keyword(s):  
Theoretical Work ◽  
Mass Splitting ◽  
Two Dimensions ◽  
Mass Generation ◽  
Dynamical Generation ◽  
Natural Outcome ◽  
Gross Neveu Model

Based on early theoretical work on tachyonic fermions we shall study a modification of the Gross–Neveu model in two dimensions. We shall see that the theory results to the dynamical generation of real and imaginary masses. These imaginary masses indicate the possibility that tachyonic solutions (or instabilities) could exist in the theory. The implications of a tachyonic neutrino coming from astrophysical sources are critically discussed. Moreover, we present a toy model that consists of an U(2, 2) invariant Dirac Lagrangian. This theory can have tachyonic masses as solutions. A natural mass splitting between the solutions is a natural outcome of the formalism.

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 Large-N quantum gauge theories in two dimensions

1993 ◽  
Vol 303 (1-2) ◽  
pp. 95-98 ◽  
Author(s):  
B. Rusakov
Keyword(s):  
Gauge Theories ◽  
Two Dimensions ◽  
Large N

scholarly journals DYNAMICAL MASS GENERATION AND CRITICAL CURVATURE IN THE O(N) NONLINEAR SIGMA MODEL

1996 ◽  
Vol 11 (19) ◽  
pp. 1569-1578
Author(s):  
DAE-YUP SONG
Keyword(s):  
Sigma Model ◽  
Three Dimensional ◽  
Nonlinear Sigma Model ◽  
Mass Generation ◽  
Dynamical Mass ◽  
Large N ◽  
Static Einstein Universe ◽  
Critical Curvature ◽  
Second Order Phase Transition ◽  
Dynamical Mass Generation

The large-N nonlinear O(N) sigma model with the curvature coupled term ξRn2 is examined on a spacetime of R1×S2 topology (three-dimensional static Einstein universe). Making use of the cutoff method, we find the renormalized effective potential which shows that, for ξ>1/8, there is a second-order phase transition. Above the critical curvature, the dynamical mass generation does not take place even in the strong-coupled regime. The phase structure of the model on S2 is also discussed.

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