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 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 (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 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 Connecting 5d Higgs branches via Fayet-Iliopoulos deformations

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Marieke van Beest ◽  
Simone Giacomelli
Keyword(s):  
Mirror Symmetry ◽  
Weak Coupling ◽  
Gauge Theories ◽  
Field Theories ◽  
Local Version ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Mirror Map

Abstract We describe how the geometry of the Higgs branch of 5d superconformal field theories is transformed under movement along the extended Coulomb branch. Working directly with the (unitary) magnetic quiver, we demonstrate a correspondence between Fayet-Iliopoulos deformations in 3d and 5d mass deformations. When the Higgs branch has multiple cones, characterised by a collection of magnetic quivers, the mirror map is not globally well-defined, however we are able to utilize the correspondence to establish a local version of mirror symmetry. We give several detailed examples of deformations, including decouplings and weak-coupling limits, in (Dn, Dn) conformal matter theories, TN theory and its parent PN, for which we find new Lagrangian descriptions given by quiver gauge theories with fundamental and anti-symmetric matter.

scholarly journals 5d SCFTs from decoupling and gluing

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Fabio Apruzzi ◽  
Sakura Schäfer-Nameki ◽  
Yi-Nan Wang
Keyword(s):  
Dimensional Reduction ◽  
Building Blocks ◽  
Low Energy ◽  
Field Theories ◽  
Flavor Symmetry ◽  
Superconformal Field Theories ◽  
Gauge Sector ◽  
Compact Surfaces ◽  
Bps States ◽  
M Theory

Abstract We systematically analyse 5d superconformal field theories (SCFTs) obtained by dimensional reduction from 6d $$ \mathcal{N} $$ N = (1, 0) SCFTs. Such theories have a realization as M-theory on a singular Calabi-Yau threefold, from which we determine the so-called combined fiber diagrams (CFD) introduced in [1–3]. The CFDs are graphs that encode the superconformal flavor symmetry, BPS states, low energy descriptions, as well as descendants upon flavor matter decoupling. To obtain a 5d SCFT from 6d, there are two approaches: the first is to consider a circle-reduction combined with mass deformations. The second is to circle-reduce and decouple an entire gauge sector from the theory. The former is applicable e.g. for very Higgsable theories, whereas the latter is required to obtain a 5d SCFT from a non-very Higgsable 6d theory. In the M-theory realization the latter case corresponds to decompactification of a set of compact surfaces in the Calabi-Yau threefold. To exemplify this we consider the 5d SCFTs that descend from non-Higgsable clusters and non-minimal conformal matter theories. Finally, inspired by the quiver structure of 6d theories, we propose a gluing construction for 5d SCFTs from building blocks and their CFDs.

scholarly journals M5-BRANES, TORIC DIAGRAMS AND GAUGE THEORY DUALITY

2013 ◽  
Vol 21 ◽  
pp. 136-137 ◽  
Author(s):  
LING BAO ◽  
ELLI POMONI ◽  
MASATO TAKI ◽  
FUTOSHI YAGI
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Gauge Theories ◽  
Topological String ◽  
Coupling Constants ◽  
Topological String Theory ◽  
Coulomb Branch ◽  
Effective Coupling ◽  
M Theory

We explore a duality between five-dimensional supersymmetric linear quiver gauge theories compactified on a circle, which are the five-dimensional uplifts of four-dimensional superconformal linear quiver theories. We find a correspondence between the gauge theory parameters of two dual theories, under which identical infrared effective coupling constants are obtained on the Coulomb branch. Two independent approaches using M-theory and the topological string theory give a consistent result.

scholarly journals Engineering a Bosonic AdS/CFT Correspondence

2003 ◽  
Vol 18 (23) ◽  
pp. 4233-4249 ◽  
Author(s):  
Sergei V. Ketov ◽  
Thorsten Leonhardt ◽  
Werner Rühl
Keyword(s):  
Field Theory ◽  
Gauge Theories ◽  
Critical Value ◽  
Closed String ◽  
Low Energy ◽  
Global Symmetry ◽  
Conformal Field ◽  
Black Hole Background ◽  
Hooft Limit ◽  
M Theory

We search for a bosonic (nonsupersymmetric) string/gauge theory correspondence by using the ten-dimensional IIB and 0B strings as a guide. Our construction is based on the low-energy bosonic string effective action modified by an extra form flux. We prove that the closed string tachyon can be stabilized in this context, when the AdS scalem L does not exceed a certain critical value, L<L c . The extra form may be nonperturbatively generated as a soliton from 3-string junctions, similarly to the known nonperturbative (Jackiw–Rebbi–'t Hooft–Hasenfratz) mechanism in gauge theories, as was recently argued by David, Minwalla and Núñez. We find a stable AdS 13×S13 solution that implies the existence of a 12-dimensional AdS-boundary conformal field theory with the SO(14) global symmetry in the large N't Hooft limit, which is similar to the recently proposed bosonic M-theory of Horowitz and Susskind. Taking the proposed bosonic AdS/CFT correspondence for granted, we generalize it to finite temperature. The corresponding "glueball" masses in higher space–time dimensions are calculated from the dilaton wave equation in the AdS black hole background.

scholarly journals Weyl invariant Jacobi forms along Higgsing trees

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Zhihao Duan ◽  
David Jaramillo Duque ◽  
Amir-Kian Kashani-Poor
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Gauge Theories ◽  
Topological String ◽  
Field Theories ◽  
Jacobi Forms ◽  
Superconformal Field Theories ◽  
Counting Functions ◽  
String Techniques

Abstract Using topological string techniques, we compute BPS counting functions of 5d gauge theories which descend from 6d superconformal field theories upon circle compactification. Such theories are naturally organized in terms of nodes of Higgsing trees. We demonstrate that the specialization of the partition function as we move from the crown to the root of a tree is determined by homomorphisms between rings of Weyl invariant Jacobi forms. Our computations are made feasible by the fact that symmetry enhancements of the gauge theory which are manifest on the massless spectrum are inherited by the entire tower of BPS particles. In some cases, these symmetry enhancements have a nice relation to the 1-form symmetry of the associated gauge theory.

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 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.

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