scholarly journals Bootstrapping the minimal $$ \mathcal{N} $$ = 1 superconformal field theory in three dimensions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Junchen Rong ◽  
Ning Su
Keyword(s):  
Field Theory ◽  
Critical Point ◽  
High Precision ◽  
Critical Exponents ◽  
Essential Role ◽  
Quantum Critical Point ◽  
Three Dimensions ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Superconformal Field Theory

Abstract We develop the numerical bootstrap technique to study the 2 + 1 dimensional $$ \mathcal{N} $$ N = 1 superconformal field theories (SCFTs). When applied to the minimal $$ \mathcal{N} $$ N = 1 SCFT, it allows us to determine its critical exponents to high precision. This model was argued in [1] to describe a quantum critical point (QCP) at the boundary of a 3 + 1D topological superconductor. More interestingly, this QCP can be reached by tuning a single parameter, where supersymmetry (SUSY) is realized as an emergent symmetry. We show that the emergent SUSY condition also plays an essential role in bootstrapping this SCFT. But performing a “two-sided” Padé re-summation of the large N expansion series, we calculate the critical exponents for Gross-Neveu-Yukawa models at N =4 and N =8.

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 Non-compact superconformal field theory and mock modular forms

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yuji Sugawara
Keyword(s):  
Field Theory ◽  
High Energy Phys ◽  
Modular Forms ◽  
High Energy ◽  
Field Theories ◽  
Two Dimensional ◽  
Superconformal Field Theories ◽  
Superconformal Field Theory ◽  
Mock Modular Forms ◽  
Mathematical Literature

Abstract One of interesting issues in two-dimensional superconformal field theories is the existence of anomalous modular transformation properties appearing in some non-compact superconformal models, corresponding to the “mock modularity” in mathematical literature. I review a series of my studies on this issue in collaboration with T. Eguchi, mainly focusing on T. Eguchi and Y. Sugawara, J. High Energy Phys. 1103, 107 (2011); J. High Energy Phys. 1411, 156 (2014); and Prog. Theor. Exp. Phys. 2016, 063B02 (2016).

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 Fibre-base duality of 5d KK theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Andreas P. Braun ◽  
Jin Chen ◽  
Babak Haghighat ◽  
Marcus Sperling ◽  
Shuhang Yang
Keyword(s):  
Field Theory ◽  
Field Theories ◽  
Quantum Field ◽  
Explicit Dependence ◽  
Superconformal Field Theories ◽  
Study Circle ◽  
Rank 2 ◽  
M Theory ◽  
Kaluza Klein ◽  
Theory Interpretation

Abstract We study circle compactifications of 6d superconformal field theories giving rise to 5d rank 1 and rank 2 Kaluza-Klein theories. We realise the resulting theories as M-theory compactifications on local Calabi-Yau 3-folds and match the prepotentials from geometry and field theory. One novelty in our approach is that we include explicit dependence on bare gauge couplings and mass parameters in the description which in turn leads to an accurate parametrisation of the prepotential including all parameters of the field theory. We find that the resulting geometries admit “fibre-base” duality which relates their six-dimensional origin with the purely five-dimensional quantum field theory interpretation. The fibre-base duality is realised simply by swapping base and fibre curves of compact surfaces in the local Calabi-Yau which can be viewed as the total space of the anti-canonical bundle over such surfaces. Our results show that such swappings precisely occur for surfaces with a zero self-intersection of the base curve and result in an exchange of the 6d and 5d pictures.

scholarly journals ANTI-DE-SITTER SPACE, BRANES, SINGLETONS, SUPERCONFORMAL FIELD THEORIES AND ALL THAT

1999 ◽  
Vol 14 (06) ◽  
pp. 815-843 ◽  
Author(s):  
M. J. DUFF
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Historical Review ◽  
De Sitter Space ◽  
Field Theories ◽  
De Sitter ◽  
Superconformal Field Theories ◽  
Conformal Field ◽  
New Approaches ◽  
The Universe

There has recently been a revival of interest in anti-de-Sitter space (AdS), brought about by the conjectured duality between physics in the bulk of AdS and a conformal field theory on the boundary. Since the whole subject of branes, singletons and superconformal field theories on the AdS boundary was an active area of research about ten years ago, we begin with a historical review, including the idea of the "membrane at the end of the universe." We then compare the old and new approaches and discuss some new results on AdS 5 × S5 and AdS 3 × S3.

scholarly journals Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective

2019 ◽  
Vol 6 (5) ◽  
Author(s):  
Cyril Closset ◽  
Michele Del Zotto ◽  
Vivek Saxena
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Low Energy ◽  
Field Theories ◽  
Isolated Singularity ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Ale Space ◽  
M Theory

We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities \mathbf{X}𝐗 and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to \mathbf{X}𝐗. Focussing on the case of toric CY singularities, we analyze the “gauge-theory phases” of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type A_{M-1}AM−1 fibered over a real line, and the map between the Kähler parameters of \mathbf{X}𝐗 and the Coulomb branch parameters of the field theory (masses and VEVs) can be read off systematically. Different type IIA “reductions” give rise to different gauge theory phases, whose existence depends on the particular (partial) resolutions of the isolated singularity \mathbf{X}𝐗. We also comment on the case of non-isolated toric singularities. Incidentally, we propose a slightly modified expression for the Coulomb-branch prepotential of 5d \mathcal{N}=1𝒩=1 gauge theories.

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