scholarly journals Spinning S-matrix bootstrap in 4d

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Aditya Hebbar ◽  
Denis Karateev ◽  
João Penedones
Keyword(s):  
Scattering Amplitudes ◽  
Scattering Amplitude ◽  
Bootstrap Method ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yukawa Couplings ◽  
S Matrix ◽  
Mandelstam Analyticity

Abstract We review unitarity and crossing constraints on scattering amplitudes for particles with spin in four dimensional quantum field theories. As an application we study two to two scattering of neutral spin 1/2 fermions in detail. Assuming Mandelstam analyticity of its scattering amplitude, we use the numerical S-matrix bootstrap method to estimate various non-perturbative bounds on quartic and cubic (Yukawa) couplings.

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 Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Dongmin Gang ◽  
Sungjoon Kim ◽  
Kimyeong Lee ◽  
Myungbo Shim ◽  
Masahito Yamazaki
Keyword(s):  
Field Theories ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Superconformal Field Theory ◽  
Three Sphere ◽  
Topological Quantum ◽  
S Matrix ◽  
Modular Data ◽  
Topological Theories

Abstract We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[$$ \mathcal{T} $$ T rank 0], to a (2+1)D interacting $$ \mathcal{N} $$ N = 4 superconformal field theory (SCFT) $$ \mathcal{T} $$ T rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = maxα (− log|$$ {S}_{0\alpha}^{\left(+\right)} $$ S 0 α + |) = maxα (− log|$$ {S}_{0\alpha}^{\left(-\right)} $$ S 0 α − |), where F is the round three-sphere free energy of $$ \mathcal{T} $$ T rank 0 and $$ {S}_{0\alpha}^{\left(\pm \right)} $$ S 0 α ± is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ 5 − 5 10 ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal $$ \mathcal{N} $$ N = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

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.

scholarly journals THERMOFIELD DYNAMICS FOR TWISTED POINCARÉ-INVARIANT FIELD THEORIES: WICK THEOREM AND S-MATRIX

2011 ◽  
Vol 26 (15) ◽  
pp. 2569-2589 ◽  
Author(s):  
MARCELO LEINEKER ◽  
AMILCAR R. QUEIROZ ◽  
ADEMIR E. SANTANA ◽  
CHRYSTIAN DE ASSIS SIQUEIRA
Keyword(s):  
Field Theory ◽  
Finite Temperature ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
S Matrix ◽  
Scalar Quantum ◽  
Wick Theorem ◽  
Wick’S Theorem ◽  
Invariant Quantum

Poincaré invariant quantum field theories can be formulated on noncommutative planes if the statistics of fields is twisted. This is equivalent to state that the coproduct on the Poincaré group is suitably twisted. In the present work we present a twisted Poincaré invariant quantum field theory at finite temperature. For that we use the formalism of thermofield dynamics (TFD). This TFD formalism is extend to incorporate interacting fields. This is a nontrivial step, since the separation in positive and negative frequency terms is no longer valid in TFD. In particular, we prove the validity of Wick's theorem for twisted scalar quantum field at finite temperature.

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.

MODULAR CONSTRUCTIONS OF QUANTUM FIELD THEORIES WITH INTERACTIONS

2000 ◽  
Vol 12 (02) ◽  
pp. 301-326 ◽  
Author(s):  
B. SCHROER AKEROYD ◽  
H.-W. WIESBROCK
Keyword(s):  
Fourier Transforms ◽  
Double Cone ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Cone Algebra ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Modular Method ◽  
Quantum Localization

We extend the previously introduced constructive modular method to nonperturbative QFT. In particular the relevance of the concept of "quantum localization" (via intersection of algebras) versus classical locality (via support properties of test functions) is explained in detail, the wedge algebras are constructed rigorously and the formal aspects of double cone algebras for d=1+1 factorizing theories are determined. The well-known on-shell crossing symmetry of the S-Matrix and of formfactors (cyclicity relation) in such theories is intimately related to the KMS properties of new quantum-local PFG (one-particle polarization-free) generators of these wedge algebras. These generators are "on-shell" and their Fourier transforms turn out to fulfill the Zamolodchikov–Faddeev algebra. As the wedge algebras contain the crossing symmetry information, the double cone algebras reveal the particle content of fields. Modular theory associates with this double cone algebra two very useful chiral conformal quantum field theories which are the algebraic versions of the light ray algebras.

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