scholarly journals ON NON-SUPERSYMMETRIC FINITE QUANTUM FIELD THEORIES

1995 ◽  
Vol 10 (10) ◽  
pp. 1507-1528
Author(s):  
PETER GRANDITS
Keyword(s):  
Gauge Group ◽  
Gauge Theories ◽  
Gauge Coupling ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Scalar Couplings ◽  
Finiteness Conditions ◽  
Yukawa Couplings ◽  
Loop Approximation ◽  
Supersymmetric Gauge

In a previous paper, requiring finiteness of Yukawa couplings in one-loop approximation, a no-go theorem for the finiteness of non-supersymmetric gauge theories with gauge group SU (n) was proven. Interestingly enough the gauge group SU(5), prominent in GUT models, was not covered by this proof. However, with somewhat more effort the no-go theorem can be extended to this case. Considering an even larger class of particle contents, we show that the number of possibly finite theories is greatly reduced. It should be stressed that our results are based upon two-loop finiteness of the gauge coupling, although in order to find really finite theories the finiteness conditions on the quartic scalar couplings have to be considered too.

scholarly journals CLIFFORD ALGEBRAS IN FINITE QUANTUM FIELD THEORIES I.

1998 ◽  
Vol 13 (13) ◽  
pp. 2047-2073
Author(s):  
WOLFGANG LUCHA ◽  
MICHAEL MOSER
Keyword(s):  
Gauge Coupling ◽  
Field Theories ◽  
Physical Parameters ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Gauge Groups ◽  
Yukawa Couplings ◽  
Simplifying Assumptions ◽  
Gauge Anomalies ◽  
Promising Type

Finite quantum field theories may be constructed from the most general renormalizable quantum field theory by forbidding, order by order in the perturbative loop expansion, all ultraviolet-divergent renormalizations of the physical parameters of the theory. The relevant finiteness conditions resulting from this requirement relate all dimensionless couplings in the theory. At first sight, Yukawa couplings which are equivalent to the generators of some Clifford algebra with identity element represent a very promising type of solutions of the condition for one-loop finiteness of the Yukawa couplings. However, under a few reasonable and simplifying assumptions about their particular structure, these Clifford-like Yukawa couplings prove to be in conflict with the requirements of one- and two-loop finiteness of the gauge coupling and of the absence of gauge anomalies, at least for all simple gauge groups up to and including rank 8.

scholarly journals TOWARDS FINITENESS WITHOUT SUPERSYMMETRY

1994 ◽  
Vol 09 (05) ◽  
pp. 711-726 ◽  
Author(s):  
HARALD SKARKE
Keyword(s):  
Gauge Coupling ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Particle Content ◽  
Yukawa Couplings

Some aspects of finite quantum field theories in 3+1 dimensions are discussed. A model with nonsupersymmetric particle content and vanishing one- and two-loop beta functions for the gauge coupling and one-loop beta functions for Yukawa couplings is presented.

NO-GO THEOREMS FOR NONSUPERSYMMETRIC FINITE QUANTUM FIELD THEORIES

1994 ◽  
Vol 09 (12) ◽  
pp. 1093-1103 ◽  
Author(s):  
PETER GRANDITS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Invariance ◽  
Field Theories ◽  
Special Role ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Finiteness Conditions ◽  
Yukawa Couplings

We consider the finiteness conditions on the Yukawa couplings of a general quantum field theory for groups SU (N). Their gauge invariance leads us to the necessary structure of the couplings, and for some cases the nonexistence of non-trivial solutions is proved. Somewhat miraculously a special role of SU(5) emerges as a possible case of evading these no-go theorems.

TOPOLOGICAL QUANTUM FIELD THEORIES ASSOCIATED TO FINITE GROUPS AND CROSSED G-SETS

1992 ◽  
Vol 01 (01) ◽  
pp. 1-20 ◽  
Author(s):  
DAVID N. YETTER
Keyword(s):  
Gauge Group ◽  
Quantum Groups ◽  
Finite Groups ◽  
Gauge Theories ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Link Invariants ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

Using methods suggested by the work of Turaev and Viro [11, 12], we provide a detailed construction of topological quantum field theories associated to finite crossed G-sets. Our construction of theories associated to finite groups fills in some details implicit in Dijkgraaf and Witten's [3] discussion of topological gauge theories with finite gauge group, while the theories associated to finite crossed G-sets simultaneously extend Dijkgraaf and Witten's [3] results to 3-manifolds equipped with links and Freyd and Yetter's [5] construction of link invariants from crossed G-sets from links in the 3-sphere to links in arbitrary 3-manifolds. Topological interpretations of the manifold and link invariants associated to these TQFT's are provided. We conclude discussion of our results as a toy model for QFT and of their relation to quantum groups.

scholarly journals THE RELATIONS BETWEEN GENERALIZED FIELDS AND SUPERFIELDS FORMALISMS OF THE BATALIN–VILKOVISKY METHOD OF QUANTIZATION

2004 ◽  
Vol 19 (14) ◽  
pp. 2339-2353 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
General Solution ◽  
Master Equation ◽  
Gauge Theories ◽  
Relativistic Particle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yang Mills ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

A general solution of the Batalin–Vilkovisky master equation was formulated in terms of generalized fields. Recently, a superfields approach of obtaining solutions of the Batalin–Vilkovisky master equation is also established. Superfields formalism is usually applied to topological quantum field theories. However, generalized fields method is suitable to find solutions of the Batalin–Vilkovisky master equation either for topological quantum field theories or the usual gauge theories like Yang–Mills theory. We show that by truncating some components of superfields with appropriate actions, generalized fields formalism of the usual gauge theories result. We demonstrate that for some topological quantum field theories and the relativistic particle both of the methods possess the same field contents and yield similar results. Inspired by the observed relations, we give the solution of the BV master equation for on-shell N=1 supersymmetric Yang–Mills theory utilizing superfields.

scholarly journals Infinite index extensions of local nets and defects

2018 ◽  
Vol 30 (02) ◽  
pp. 1850002 ◽  
Author(s):  
Simone Del Vecchio ◽  
Luca Giorgetti
Keyword(s):  
Gauge Theories ◽  
Von Neumann Algebras ◽  
Index Case ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Infinite Index ◽  
Von Neumann ◽  
Jones Index ◽  
The Family ◽  
Internal Symmetries

The subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [62] to the case of extensions with infinite Jones index. This case naturally arises in physics, the canonical examples are given by global gauge theories with respect to a compact (non-finite) group of internal symmetries. Building on the works of Izumi–Longo–Popa [44] and Fidaleo–Isola [30], we consider generalized Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite von Neumann algebras, which generalize ordinary Q-systems introduced by Longo [58] to the infinite index case. We characterize inclusions which admit generalized Q-systems of intertwiners and define a braided product among the latter, hence we construct examples of QFTs with defects (phase boundaries) of infinite index, extending the family of boundaries in the grasp of [7].

scholarly journals DIFF(Σ) AND METRICS FROM HAMILTONIAN-TQFT'S IN 2+1 DIMENSIONS

1993 ◽  
Vol 08 (24) ◽  
pp. 2277-2283 ◽  
Author(s):  
ROGER BROOKS
Keyword(s):  
Topological Field Theories ◽  
Gauge Theories ◽  
Dimensional Space ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Canonical Gravity ◽  
Topological Quantum ◽  
Topological Field

The constraints of BF topological gauge theories are used to construct Hamiltonians which are anti-commutators of the BRST and anti-BRST operators. Such Hamiltonians are a signature of topological quantum field theories (TQFTs). By construction, both classes of topological field theories share the same phase spaces and constraints. We find that, for (2+1)- and (1+1)-dimensional space-times foliated as M=Σ × ℝ, a homomorphism exists between the constraint algebras of our TQFT and those of canonical gravity. The metrics on the two-dimensional hypersurfaces are also obtained.

scholarly journals TOWARDS A CLASSIFICATION OF FINITE FIELD THEORIES

1994 ◽  
Vol 09 (27) ◽  
pp. 2555-2567
Author(s):  
PETER GRANDITS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Field ◽  
Field Theories ◽  
Quantum Field ◽  
Particle Content ◽  
Finiteness Conditions ◽  
Gauge Groups ◽  
Yukawa Couplings

We consider the finiteness conditions on the Yukawa couplings of a general quantum field theory for gauge groups SU (n)(n>6) and a rather general particle content. It is shown that in the class of theories considered (149 different particle contents), only two models are able to fulfill the finiteness conditions. Only one of these is supersymmetric. For the nonsupersymmetric one the appropriate Yukawa couplings are constructed explicitly.

scholarly journals NONPERTURBATIVE EFFECTIVE ACTIONS OF (N=2)-SUPERSYMMETRIC GAUGE THEORIES

1996 ◽  
Vol 11 (11) ◽  
pp. 1929-1973 ◽  
Author(s):  
A. KLEMM ◽  
W. LERCHE ◽  
S. THEISEN
Keyword(s):  
Riemann Surface ◽  
Effective Action ◽  
Gauge Theories ◽  
Gauge Coupling ◽  
Low Energy ◽  
Yang Mills ◽  
Hyperelliptic Riemann Surface ◽  
Supersymmetric Gauge ◽  
Energy Quantum ◽  
Appell Functions

We elaborate on our previous work on (N=2)-supersymmetric Yang-Mills theory. In particular, we show how to explicitly determine the low energy quantum effective action for G=SU(3) from the underlying hyperelliptic Riemann surface, and calculate the leading instanton corrections. This is done by solving Picard-Fuchs equations and asymptotically evaluating period integrals. We find that the dynamics of the SU(3) theory is governed by an Appell system of type F4, and compute the exact quantum gauge coupling explicitly in terms of Appell functions.

DOES STOCHASTIC ANALYTIC REGULARIZATION PROVIDE QUANTUM FIELD THEORIES?

1992 ◽  
Vol 07 (04) ◽  
pp. 777-794
Author(s):  
C. P. MARTIN
Keyword(s):  
Field Theory ◽  
Regularization Method ◽  
Gauge Theories ◽  
Field Theories ◽  
Intermediate Step ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Point Function ◽  
Four Dimensions ◽  
Analytic Regularization

We analyze whether the so-called method of stochastic analytic regularization is suitable as an intermediate step for constructing perturbative renormalized quantum field theories. We choose a λϕ3 in six dimensions to prove that this regularization method does not in general provide a quantum field theory. This result seems to apply to any field theory with a quadratically UV-divergent stochastic two-point function, for instance λϕ4 and gauge theories in four dimensions.

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