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 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 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 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 5d and 4d SCFTs: canonical singularities, trinions and S-dualities

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Cyril Closset ◽  
Simone Giacomelli ◽  
Sakura Schäfer-Nameki ◽  
Yi-Nan Wang
Keyword(s):  
String Theory ◽  
Field Theories ◽  
Flavor Symmetry ◽  
Crepant Resolution ◽  
Superconformal Field Theories ◽  
Hypersurface Singularities ◽  
Canonical Singularities ◽  
Type Iib String Theory ◽  
M Theory

Abstract Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of ‘trinion’ singularities which exhibit these properties. In Type IIB, they give rise to 4d $$ \mathcal{N} $$ N = 2 SCFTs that we call $$ {D}_p^b $$ D p b (G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d $$ \mathcal{N} $$ N = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as ‘ugly’ components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver ‘bad’. We propose a way to redeem the badness of these quivers using a class $$ \mathcal{S} $$ S realization. We also discover new S-dualities between different $$ {D}_p^b $$ D p b (G)-trinions. For instance, a certain E8 gauging of the E8 Minahan-Nemeschansky theory is S-dual to an E8-shaped Lagrangian quiver SCFT.

scholarly journals (Symplectic) leaves and (5d Higgs) branches in the Poly(go)nesian Tropical Rain Forest

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Marieke van Beest ◽  
Antoine Bourget ◽  
Julius Eckhard ◽  
Sakura Schäfer-Nameki
Keyword(s):  
Rain Forest ◽  
Tropical Rain Forest ◽  
Gauge Theories ◽  
Edge Coloring ◽  
Field Theories ◽  
Minkowski Sum ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Minkowski Sums ◽  
Symplectic Leaves

Abstract We derive the structure of the Higgs branch of 5d superconformal field theories or gauge theories from their realization as a generalized toric polygon (or dot diagram). This approach is motivated by a dual, tropical curve decomposition of the (p, q) 5-brane-web system. We define an edge coloring, which provides a decomposition of the generalized toric polygon into a refined Minkowski sum of sub-polygons, from which we compute the magnetic quiver. The Coulomb branch of the magnetic quiver is then conjecturally identified with the 5d Higgs branch. Furthermore, from partial resolutions, we identify the symplectic leaves of the Higgs branch and thereby the entire foliation structure. In the case of strictly toric polygons, this approach reduces to the description of deformations of the Calabi-Yau singularities in terms of Minkowski sums.

scholarly journals M5-brane sources, holography, and Argyres-Douglas theories

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Ibrahima Bah ◽  
Federico Bonetti ◽  
Ruben Minasian ◽  
Emily Nardoni
Keyword(s):  
Warped Product ◽  
Central Charge ◽  
Field Theories ◽  
Internal Space ◽  
Flavor Symmetry ◽  
Perfect Agreement ◽  
Strongly Coupled ◽  
Superconformal Field Theories ◽  
Holographic Duals ◽  
M Theory

Abstract We initiate a study of the holographic duals of a class of four-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories that are engineered by wrapping M5-branes on a sphere with an irregular puncture. These notably include the strongly-coupled field theories of Argyres-Douglas type. Our solutions are obtained in 7d gauged supergravity, where they take the form of a warped product of AdS5 and a “half-spindle.” The irregular puncture is modeled by a localized M5-brane source in the internal space of the gravity duals. Our solutions feature a realization of supersymmetry that is distinct from the usual topological twist, as well as an interesting Stückelberg mechanism involving the gauge field associated to a generator of the isometry algebra of the internal space. We check the proposed duality by computing the holographic central charge, the flavor symmetry central charge, and the dimensions of various supersymmetric probe M2-branes, and matching these with the dual Argyres-Douglas field theories. Furthermore, we compute the large-N ’t Hooft anomalies of the field theories using anomaly inflow methods in M-theory, and find perfect agreement with the proposed duality.

scholarly journals Non-simply-connected symmetries in 6D SCFTs

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Markus Dierigl ◽  
Paul-Konstantin Oehlmann ◽  
Fabian Ruehle
Keyword(s):  
Abelian Group ◽  
Large Class ◽  
Group Structure ◽  
Field Theories ◽  
Symmetry Groups ◽  
Superconformal Field Theories ◽  
Weil Group ◽  
Superconformal Theories ◽  
Simply Connected ◽  
M Theory

Abstract Six-dimensional $$ \mathcal{N} $$ N = (1, 0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This allows us to identify the full non-Abelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.

scholarly journals Flavor symmetry of 5d SCFTs. Part I. General setup

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Lakshya Bhardwaj
Keyword(s):  
Large Class ◽  
Field Theories ◽  
Flavor Symmetry ◽  
Superconformal Field Theories ◽  
Compact Surfaces ◽  
M Theory ◽  
General Setup ◽  
General Method

Abstract A large class of 5d superconformal field theories (SCFTs) can be constructed by integrating out BPS particles from 6d SCFTs compactified on a circle. We describe a general method for extracting the flavor symmetry of any 5d SCFT lying in this class. For this purpose, we utilize the geometric engineering of 5d$$ \mathcal{N} $$ N = 1 theories in M-theory, where the flavor symmetry is encoded in a collection of non-compact surfaces.

scholarly journals New $$ \mathcal{N} $$ = 2 superconformal field theories from $$ \mathcal{S} $$-folds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Simone Giacomelli ◽  
Carlo Meneghelli ◽  
Wolfger Peelaers
Keyword(s):  
Moduli Spaces ◽  
Field Theories ◽  
Coulomb Branch ◽  
Infinite Class ◽  
Superconformal Field Theories ◽  
New Class

Abstract We study the four-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories that describe D3-branes probing the recently constructed $$ \mathcal{N} $$ N = 2 $$ \mathcal{S} $$ S -folds in F-theory. We introduce a novel, infinite class of superconformal field theories related to $$ \mathcal{S} $$ S -fold theories via partial Higgsing. We determine several properties of both the $$ \mathcal{S} $$ S -fold models and this new class of theories, including their central charges, Coulomb branch spectrum, and moduli spaces of vacua, by bringing to bear an array of field-theoretical techniques, to wit, torus-compactifications of six-dimensional $$ \mathcal{N} $$ N = (1, 0) theories, class $$ \mathcal{S} $$ S technology, and the SCFT/VOA correspondence.

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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