ON ϵ-CONJECTURE IN a-THEOREM

The derivation of the a-theorem recently proposed by Komargodski and Schwimmer relies on the ϵ-conjecture that demands decoupling of dilaton from the rest of the infrared theory. We point out that the decoupling, if true, provides a strong evidence for the equivalence between scale invariance and conformal invariance in four dimensions. Thus, a complete proof of the a-theorem along the line of their argument in the most generic scenario would establish the equivalence between scale invariance and conformal invariance, which is another long-standing conjecture in four-dimensional quantum field theories.

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DOES STOCHASTIC ANALYTIC REGULARIZATION PROVIDE QUANTUM FIELD THEORIES?

International Journal of Modern Physics A ◽

10.1142/s0217751x92000375 ◽

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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Topological Quantum Field Theories in Four Dimensions

Topological Quantum Field Theory and Four Manifolds - Mathematical Physics Studies ◽

10.1007/1-4020-3177-7_5 ◽

2007 ◽

pp. 58-77

Keyword(s):

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Four Dimensions ◽

Topological Quantum ◽

Topological Quantum Field Theories

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Higher form symmetries and M-theory

Journal of High Energy Physics ◽

10.1007/jhep12(2020)203 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Federica Albertini ◽

Michele Del Zotto ◽

Iñaki García Etxebarria ◽

Saghar S. Hosseini

Keyword(s):

Defect Group ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Consistency Check ◽

Four Dimensions ◽

Defect Groups ◽

Geometric Origin ◽

M Theory

Abstract We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory gives rise to (mixed) ’t Hooft anomalies for the defect group which constrains the corresponding global structures of the associated quantum fields. We analyze the example of 4d $$ \mathcal{N} $$ N = 1 SYM gauge theory in four dimensions, and we reproduce the well-known classification of global structures from reading between its lines. We extend this analysis to the case of 7d $$ \mathcal{N} $$ N = 1 SYM theory, where we recover it from a mixed ’t Hooft anomaly among the electric 1-form center symmetry and the magnetic 4-form center symmetry in the defect group. The case of five-dimensional SCFTs from M-theory on toric singularities is discussed in detail. In that context we determine the corresponding 1-form and 2-form defect groups and we explain how to determine the corresponding mixed ’t Hooft anomalies from flux non-commutativity. Several predictions for non-conventional 5d SCFTs are obtained. The matching of discrete higher-form symmetries and their anomalies provides an interesting consistency check for 5d dualities.

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Instantons beyond topological theory. I

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s1474748011000077 ◽

2011 ◽

Vol 10 (3) ◽

pp. 463-565 ◽

Cited By ~ 7

Author(s):

E. Frenkel ◽

A. Losev ◽

N. Nekrasov

Keyword(s):

Correlation Functions ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Conformal Field Theories ◽

Four Dimensions ◽

Yang Mills ◽

Conformal Field ◽

Mechanical Models ◽

Perturbative Corrections

AbstractMany quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyse the corresponding models as full quantum field theories, beyond their topological sector. We show that the correlation functions of all, not only topological (or BPS), observables may be studied explicitly in these models, and the spectrum may be computed exactly. An interesting feature is that the Hamiltonian is not always diagonalizable, but may have Jordan blocks, which leads to the appearance of logarithms in the correlation functions. We also find that in the models defined on Kähler manifolds the space of states exhibits holomorphic factorization. We conclude that in dimensions two and four our theories are logarithmic conformal field theories.In Part I we describe the class of models under study and present our results in the case of one-dimensional (quantum mechanical) models, which is quite representative and at the same time simple enough to analyse explicitly. Part II will be devoted to supersymmetric two-dimensional sigma models and four-dimensional Yang–Mills theory. In Part III we will discuss non-supersymmetric models.

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Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

Zeitschrift für Naturforschung A ◽

10.1515/zna-1985-0717 ◽

1985 ◽

Vol 40 (7) ◽

pp. 752-773

Author(s):

H. Stumpf

Keyword(s):

Composite Particle ◽

Particle Interaction ◽

High Energy ◽

Field Theories ◽

Quantum Field Theories ◽

Statistical Interpretation ◽

Quantum Field ◽

Mapping Procedure ◽

Effective Dynamics ◽

Rough Approximation

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

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Categorification of algebraic quantum field theories

Letters in Mathematical Physics ◽

10.1007/s11005-021-01371-8 ◽

2021 ◽

Vol 111 (2) ◽

Author(s):

Marco Benini ◽

Marco Perin ◽

Alexander Schenkel ◽

Lukas Woike

Keyword(s):

Universal Algebra ◽

Finite Groups ◽

Physical Interpretation ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Algebraic Quantum

AbstractThis paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen’s universal algebra is developed and also computed for simple examples of 2AQFTs.

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