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.

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 Twisted circle compactifications of 6d SCFTs

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Lakshya Bhardwaj ◽  
Patrick Jefferson ◽  
Hee-Cheol Kim ◽  
Houri-Christina Tarazi ◽  
Cumrun Vafa
Keyword(s):  
Field Theories ◽  
Geometric Description ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Physical Data ◽  
Algebraic Description ◽  
Genus One ◽  
M Theory ◽  
Kaluza Klein

Abstract We study 6d superconformal field theories (SCFTs) compactified on a circle with arbitrary twists. The theories obtained after compactification, often referred to as 5d Kaluza-Klein (KK) theories, can be viewed as starting points for RG flows to 5d SCFTs. According to a conjecture, all 5d SCFTs can be obtained in this fashion. We compute the Coulomb branch prepotential for all 5d KK theories obtainable in this manner and associate to these theories a smooth local genus one fibered Calabi-Yau threefold in which is encoded information about all possible RG flows to 5d SCFTs. These Calabi-Yau threefolds provide hitherto unknown M-theory duals of F-theory configurations compactified on a circle with twists. For certain exceptional KK theories that do not admit a standard geometric description we propose an algebraic description that appears to retain the properties of the local Calabi-Yau threefolds necessary to determine RG flows to 5d SCFTs, along with other relevant physical data.

scholarly journals (5d RG-flow) trees in the tropical rain forest

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Marieke van Beest ◽  
Antoine Bourget ◽  
Julius Eckhard ◽  
Sakura Schäfer-Nameki
Keyword(s):  
Large Class ◽  
Rain Forest ◽  
Tropical Rain Forest ◽  
Field Theories ◽  
Flavor Symmetry ◽  
Superconformal Field Theories ◽  
Hasse Diagrams ◽  
Flavor Symmetries ◽  
Rank 2 ◽  
Mass Deformation

Abstract 5d superconformal field theories (SCFTs) can be obtained from 6d SCFTs by circle compactification and mass deformation. Successive decoupling of hypermultiplet matter and RG-flow generates a decoupling tree of descendant 5d SCFTs. In this paper we determine the magnetic quivers and Hasse diagrams, that encode the Higgs branches of 5d SCFTs, for entire decoupling trees. Central to this undertaking is the approach in [1], which, starting from the generalized toric polygons (GTPs) dual to 5-brane webs/tropical curves, provides a systematic and succinct derivation of magnetic quivers and their Hasse diagrams. The decoupling in the GTP description is straightforward, and generalizes the standard flop transitions of curves in toric polygons. We apply this approach to a large class of 5d KK-theories, and compute the Higgs branches for their descendants. In particular we determine the decoupling tree for all rank 2 5d SCFTs. For each tree, we also identify the flavor symmetry algebras from the magnetic quivers, including non-simply-laced flavor symmetries.

scholarly journals Exceptional Chern-Simons-Matter dualities

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Clay Cordova ◽  
Po-Shen Hsin ◽  
Kantaro Ohmori
Keyword(s):  
Gauge Theory ◽  
Topological Field Theories ◽  
Time Reversal ◽  
Three Dimensional ◽  
Field Theories ◽  
Chiral Algebra ◽  
Gauge Groups ◽  
Topological Field ◽  
Conformal Embeddings ◽  
Chern Simons

We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is (E_{N})_{1}\leftrightarrow SU(9-N)_{-1}(EN)1↔SU(9−N)−1. Others such as SO(3)_{8}\leftrightarrow PSU(3)_{-6},SO(3)8↔PSU(3)−6, are dualities among theories with classical gauge groups that arise due to their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons-matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant G_{2}G2 gauge theory coupled to either an adjoint fermion, or two fundamental fermions.

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.

scholarly journals GAUGE THEORY DEFORMATIONS AND NOVEL YANG–MILLS CHERN–SIMONS FIELD THEORIES WITH TORSION

2004 ◽  
Vol 01 (04) ◽  
pp. 493-544 ◽  
Author(s):  
STEPHEN C. ANCO
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Covariant Derivative ◽  
Gauge Theories ◽  
Field Theories ◽  
Deformation Method ◽  
Yang Mills ◽  
The Past ◽  
Nonlinear Gauge ◽  
Chern Simons

A basic problem of classical field theory, which has attracted growing attention over the past decade, is to find and classify all nonlinear deformations of linear abelian gauge theories. The physical interest in studying deformations is to address uniqueness of known nonlinear interactions of gauge fields and to look systematically for theoretical possibilities for new interactions. Mathematically, the study of deformations aims to understand the rigidity of the nonlinear structure of gauge field theories and to uncover new types of nonlinear geometrical structures. The first part of this paper summarizes and significantly elaborates a field-theoretic deformation method developed in earlier work. Some key contributions presented here are, firstly, that the determining equations for deformation terms are shown to have an elegant formulation using Lie derivatives in the jet space associated with the gauge field variables. Secondly, the obstructions (integrability conditions) that must be satisfied by lowest-order deformations terms for existence of a deformation to higher orders are explicitly identified. Most importantly, a universal geometrical structure common to a large class of nonlinear gauge theory examples is uncovered. This structure is derived geometrically from the deformed gauge symmetry and is characterized by a covariant derivative operator plus a nonlinear field strength, related through the curvature of the covariant derivative. The scope of these results encompasses Yang–Mills theory, Freedman–Townsend theory, and Einstein gravity theory, in addition to their many interesting types of novel generalizations that have been found in the past several years. The second part of the paper presents a new geometrical type of Yang–Mills generalization in three dimensions motivated from considering torsion in the context of nonlinear sigma models with Lie group targets (chiral theories). The generalization is derived by a deformation analysis of linear abelian Yang–Mills Chern–Simons gauge theory. Torsion is introduced geometrically through a duality with chiral models obtained from the chiral field form of self-dual (2+2) dimensional Yang–Mills theory under reduction to (2+1) dimensions. Field-theoretic and geometric features of the resulting nonlinear gauge theories with torsion are discussed.

scholarly journals On the compactification of 5d theories to 4d

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Mario Martone ◽  
Gabi Zafrir
Keyword(s):  
Strong Coupling ◽  
Moduli Spaces ◽  
Integrable Systems ◽  
Strong Coupling Limit ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
General Properties ◽  
Rank 2 ◽  
Mass Deformation

Abstract We study general properties of the mapping between 5d and 4d superconformal field theories (SCFTs) under both twisted circle compactification and tuning of local relevant deformation and CB moduli. After elucidating in generality when a 5d SCFT reduces to a 4d one, we identify nearly all $$ \mathcal{N} $$ N = 1 5d SCFT parents of rank-2 4d$$ \mathcal{N} $$ N = 2 SCFTs. We then use this result to map out the mass deformation trajectories among the rank-2 theories in 4d. This can be done by first understanding the mass deformations of the 5d$$ \mathcal{N} $$ N = 1 SCFTs and then map them to 4d. The former task can be easily achieved by exploiting the fact that the 5d parent theories can be obtained as the strong coupling limit of Lagrangian theories, and the latter by understanding the behavior under compactification. Finally we identify a set of general criteria that 4d moduli spaces of vacua have to satisfy when the corresponding SCFTs are related by mass deformations and check that all our RG-flows satisfy them. Many of the mass deformations we find are not visible from the corresponding complex integrable systems.

scholarly journals 4D Chern–Simons theory and affine Gaudin models

2021 ◽  
Vol 111 (1) ◽  
Author(s):  
Benoît Vicedo
Keyword(s):  
Gauge Theory ◽  
Integrable Field Theories ◽  
Field Theories ◽  
Simons Theory ◽  
Gaudin Models ◽  
Chern Simons ◽  
Classical Integrable ◽  
Integrable Field ◽  
Chern Simons Theory

AbstractWe relate two formalisms recently proposed for describing classical integrable field theories. The first (Costello and Yamazaki in Gauge Theory and Integrability, III, 2019) is based on the action of four-dimensional Chern–Simons theory introduced and studied by Costello, Witten and Yamazaki. The second (Costello and Yamazaki, in Gauge Theory and Integrability, III, 2017) makes use of classical generalised Gaudin models associated with untwisted affine Kac–Moody algebras.

scholarly journals Proving the 6d Cardy formula and matching global gravitational anomalies

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Chi-Ming Chang ◽  
Martin Fluder ◽  
Ying-Hsuan Lin ◽  
Yifan Wang
Keyword(s):  
Free Field ◽  
Fractional Part ◽  
Additional Contribution ◽  
Coulomb Branch ◽  
Gauge Invariant ◽  
Superconformal Field Theories ◽  
Chern Simons ◽  
Cardy Formula ◽  
Kaluza Klein ◽  
Gravitational Anomalies

A Cardy formula for 6d superconformal field theories (SCFTs) conjectured by Di Pietro and Komargodski in [1] governs the universal behavior of the supersymmetric partition function on S^1_\beta \times S^5Sβ1×S5 in the limit of small \betaβ and fixed squashing of the S^5S5. For a general 6d SCFT, we study its 5d effective action, which is dominated by the supersymmetric completions of perturbatively gauge-invariant Chern-Simons terms in the small \betaβ limit. Explicitly evaluating these supersymmetric completions gives the precise squashing dependence in the Cardy formula. For SCFTs with a pure Higgs branch (also known as very Higgsable SCFTs), we determine the Chern-Simons levels by explicitly going onto the Higgs branch and integrating out the Kaluza-Klein modes of the 6d fields on S^1_\betaSβ1. We then discuss tensor branch flows, where an apparent mismatch between the formula in [1] and the free field answer requires an additional contribution from BPS strings. This ``missing contribution’’ is further sharpened by the relation between the fractional part of the Chern-Simons levels and the (mixed) global gravitational anomalies of the 6d SCFT. We also comment on the Cardy formula for 4d \mathcal{N}=2𝒩=2 SCFTs in relation to Higgs branch and Coulomb branch flows.

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