scholarly journals Compactifying 5d superconformal field theories to 3d

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Matteo Sacchi ◽  
Orr Sela ◽  
Gabi Zafrir
Keyword(s):  
Riemann Surfaces ◽  
Recent Progress ◽  
Three Dimensions ◽  
Field Theories ◽  
Global Symmetry ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
The One ◽  
Conformal Manifolds ◽  
Chern Simons

Abstract Building on recent progress in the study of compactifications of 6d (1, 0) superconformal field theories (SCFTs) on Riemann surfaces to 4d$$ \mathcal{N} $$ N = 1 theories, we initiate a systematic study of compactifications of 5d$$ \mathcal{N} $$ N = 1 SCFTs on Riemann surfaces to 3d$$ \mathcal{N} $$ N = 2 theories. Specifically, we consider the compactification of the so-called rank 1 Seiberg $$ {E}_{N_f+1} $$ E N f + 1 SCFTs on tori and tubes with flux in their global symmetry, and put the resulting 3d theories to various consistency checks. These include matching the (usually enhanced) IR symmetry of the 3d theories with the one expected from the compactification, given by the commutant of the flux in the global symmetry of the corresponding 5d SCFT, and identifying the spectrum of operators and conformal manifolds predicted by the 5d picture. As the models we examine are in three dimensions, we encounter novel elements that are not present in compactifications to four dimensions, notably Chern-Simons terms and monopole superpotentials, that play an important role in our construction. The methods used in this paper can also be used for the compactification of any other 5d SCFT that has a deformation leading to a 5d gauge theory.

scholarly journals A CFT distance conjecture

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Eric Perlmutter ◽  
Leonardo Rastelli ◽  
Cumrun Vafa ◽  
Irene Valenzuela
Keyword(s):  
Spin Symmetry ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Higher Spin ◽  
Spin Fields ◽  
Local Operators ◽  
Conformal Manifolds

Abstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

scholarly journals A STRONG COUPLING EXPANSION FOR N = 4 SYM THEORY AND OTHER SCFT's

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2143-2152 ◽  
Author(s):  
DAVID BERENSTEIN
Keyword(s):  
Wave Function ◽  
Strong Coupling ◽  
Recent Progress ◽  
Einstein Manifold ◽  
Strong Coupling Expansion ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills

Recent progress towards understanding a strong coupling expansion for various superconformal field theories in four dimensions is described. First, the case of the maximally supersymmetric Yang Mills theory is analyzed, as well as many calculations that can be done directly at strong coupling and matched to the AdS dual geometry. Also, this understanding is extended to other AdS duals where the sphere is replaced by a Sasaki-Einstein manifold. Particular emphasis is made on matching exactly part of the supergravity dual spectrum of various of these field theories by using wave function methods.

scholarly journals Chiral correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Galvagno ◽  
Michelangelo Preti
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Flat Space ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
The Matrix ◽  
Superspace Formalism ◽  
Model Approach

Abstract We consider a family of $$ \mathcal{N} $$ N = 2 superconformal field theories in four dimensions, defined as ℤq orbifolds of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $$ \mathcal{N} $$ N = 1 superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of N , exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from $$ \mathcal{N} $$ N = 4 only at high orders in perturbation theory.

scholarly journals Non-invertible global symmetries and completeness of the spectrum

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Ben Heidenreich ◽  
Jacob McNamara ◽  
Miguel Montero ◽  
Matthew Reece ◽  
Tom Rudelius ◽  
...  
Keyword(s):  
Gauge Theories ◽  
Cosmic Strings ◽  
Global Symmetry ◽  
Complete Spectrum ◽  
Abelian Gauge ◽  
Analogous Statement ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Chern Simons ◽  
General Gauge

Abstract It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.

RENORMALIZATION OF STOCHASTICALLY QUANTIZED FIELD THEORIES

1988 ◽  
Vol 03 (01) ◽  
pp. 163-185 ◽  
Author(s):  
S. CHATURVEDI ◽  
A.K. KAPOOR ◽  
V. SRINIVASAN
Keyword(s):  
Langevin Equation ◽  
Field Theories ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Coupling Constant ◽  
Operator Formalism ◽  
Four Dimensions ◽  
Quantized Field ◽  
The One ◽  
Renormalization Constants

We discuss the renormalizability of stochastically quantized ϕ4 theory in four dimensions using the operator formalism of the Langevin equation developed by Namiki and Yamanaka. The operator formalism casts the Parisi Wu stochastic quantization scheme into a five-dimensional field theory. The usefulness of this approach over the one based directly on the Langevin equation is brought out for discussion of renormalization. We propose a new regularization scheme for the stochastic diagrams and use it to compute the renormalization constants and counter terms for the ϕ4 theory to second order in the coupling constant.

N=2 SUPERSTRING THEORY GENERATES SUPERSYMMETRIC CHERN-SIMONS THEORIES

1994 ◽  
Vol 09 (35) ◽  
pp. 3255-3266 ◽  
Author(s):  
HITOSHI NISHINO
Keyword(s):  
Integrable Models ◽  
Three Dimensions ◽  
Superstring Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Fundamental Significance ◽  
Background Fields ◽  
Chern Simons

We show that the action of self-dual supersymmetric Yang-Mills theory in four dimensions, which describes the consistent massless background fields for N=2 superstring, generates the actions for N=1 and N=2 supersymmetric non-Abelian Chern-Simons theories in three dimensions after some dimensional reductions. Since the latters play important roles for supersymmetric integrable models, this result indicates the fundamental significance of the N=2 superstring theory controlling (possibly all) supersymmetric integrable models in lower dimensions.

scholarly journals Correlation functions of spinor current multiplets in $$ \mathcal{N} $$ = 1 superconformal theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Evgeny I. Buchbinder ◽  
Jessica Hutomo ◽  
Sergei M. Kuzenko
Keyword(s):  
Field Theory ◽  
Correlation Functions ◽  
Field Theories ◽  
Point Function ◽  
Superconformal Field Theories ◽  
Superconformal Symmetry ◽  
Four Dimensions ◽  
Superconformal Field Theory ◽  
Superconformal Theories ◽  
Spinor Current

Abstract We consider $$ \mathcal{N} $$ N = 1 superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet Sα and study three-point functions involving such an operator. A conserved spinor current multiplet naturally exists in superconformal theories with $$ \mathcal{N} $$ N = 2 supersymmetry and contains the current of the second supersymmetry. However, we do not assume $$ \mathcal{N} $$ N = 2 supersymmetry. We show that the three-point function of two spinor current multiplets and the $$ \mathcal{N} $$ N = 1 supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the $$ \mathcal{N} $$ N = 2 supercurrent. It then follows, based on symmetry considerations only, that the existence of one more Grassmann odd current multiplet in $$ \mathcal{N} $$ N = 1 superconformal field theory does not necessarily imply $$ \mathcal{N} $$ N = 2 superconformal symmetry.

scholarly journals New = 2 superconformal field theories in four dimensions

1996 ◽  
Vol 461 (1-2) ◽  
pp. 71-84 ◽  
Author(s):  
Philip C Argyres ◽  
M Ronen Plesser ◽  
Nathan Seiberg ◽  
Edward Witten
Keyword(s):  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions

scholarly journals Bootstrapping BPS spectra of 5d/6d field theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hee-Cheol Kim ◽  
Minsung Kim ◽  
Sung-Soo Kim ◽  
Ki-Hong Lee
Keyword(s):  
Gauge Theory ◽  
Systematic Approach ◽  
Field Theories ◽  
Geometric Description ◽  
Superconformal Field Theories ◽  
Significant Generalization ◽  
Rank 2 ◽  
Bps Spectrum ◽  
Chern Simons ◽  
Kaluza Klein

Abstract We propose a systematic approach to computing the BPS spectrum of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka’s blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup $$ \hat{\mathrm{\mathbb{C}}} $$ ℂ ̂ 2 and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d $$ \mathcal{N} $$ N = (1, 0) superconformal field theories (SCFTs) compactified on a circle with/without twist. We also discuss various 5d SCFTs and KK theories of higher ranks, which include a few exotic cases such as new rank-1 and rank-2 5d SCFTs engineered with frozen singularity as well as the 5d SU(3)8 gauge theory currently having neither a brane web nor a smooth shrinkable geometric description. The results serve as non-trivial checks for a large class of non-trivial dualities among 5d theories and also as independent evidences for the existence of certain exotic theories.

Sign in / Sign up

Export Citation Format

Share Document