A
bstract
We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on their realization as M-theory compactifications on singular elliptic Calabi-Yau threefolds. ...Field-theoretically, these 5d SCFTs descend from 6d
N
= (1
,
0) SCFTs by circle compactification and mass deformations. We derive a description of these theories in terms of graphs, so-called Combined Fiber Diagrams, which encode salient features of the partially resolved Calabi-Yau geometry, and provides a combinatorial way of characterizing all 5d SCFTs that descend from a given 6d theory. Remarkably, these graphs manifestly capture strongly coupled data of the 5d SCFTs, such as the superconformal flavor symmetry, BPS states, and mass deformations. The capabilities of this approach are demonstrated by deriving all rank one and rank two 5d SCFTs. The full potential, how- ever, becomes apparent when applied to theories with higher rank. Starting with the higher rank conformal matter theories in 6d, we are led to the discovery of previously unknown flavor symmetry enhancements and new 5d SCFTs.
Recent work has established a uniform characterization of most 6D SCFTs in terms of generalized quivers with conformal matter. Compactification of the partial tensor branch deformation of these ...theories on a T2 leads to 4D N=2 SCFTs which are also generalized quivers. Taking products of bifundamental conformal matter operators, we present evidence that there are large R-charge sectors of the theory in which operator mixing is captured by a 1D spin chain Hamiltonian with operator scaling dimensions controlled by a perturbation series in inverse powers of the R-charge. We regulate the inherent divergences present in the 6D computations with the associated 5D Kaluza–Klein theory. In the case of 6D SCFTs obtained from M5-branes probing a C2/ZK singularity, we show that there is a class of operators where the leading order mixing effects are captured by the integrable Heisenberg XXXs=1/2 spin chain with open boundary conditions, and similar considerations hold for its T2 reduction to a 4D N=2 SCFT. In the case of M5-branes probing more general D- and E-type singularities where generalized quivers have conformal matter, we argue that similar mixing effects are captured by an integrable XXXs spin chain with s>1/2. We also briefly discuss some generalizations to other operator sectors as well as little string theories.
F-theory and AdS3/CFT2 Couzens, Christopher; Lawrie, Craig; Martelli, Dario ...
The journal of high energy physics,
08/2017, Volume:
2017, Issue:
8
Journal Article
Peer reviewed
Open access
A
bstract
We construct supersymmetric AdS
3
solutions in F-theory, that is Type IIB supergravity with varying axio-dilaton, which are holographically dual to 2d
N
=
0
4
superconformal field theories ...with small superconformal algebra. In F-theory these arise from D3-branes wrapped on curves in the base of an elliptically fibered Calabi-Yau threefold
Y
3
and correspond to self-dual strings in the 6d
N
=
1
0
theory obtained from F-theory on
Y
3
. The non-trivial fibration over the wrapped curves implies a varying coupling of the
N
=
4
Super-Yang-Mills theory on the D3-branes. We compute the holographic central charges and show that these agree with the field theory and with the anomalies of self-dual strings in 6d. We complement our analysis with a discussion of the dual M-theory solutions and a comparison of the central charges.
A
bstract
In 1, 2 we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d
N
= (1
,
0) SCFTs. The graphs, so-called ...combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi-Yau threefold with a canonical singularity. In this paper we complement this geometric approach by connecting the CFD of an SCFT to its weakly coupled gauge theory or quiver descriptions and demonstrate that the CFD as recovered from the gauge theory approach is consistent with that as determined by geometry. To each quiver description we also associate a graph, and the embedding of this graph into the CFD that is associated to an SCFT provides a systematic way to enumerate all possible consistent weakly coupled gauge theory descriptions of this SCFT. Furthermore, different embeddings of gauge theory graphs into a fixed CFD can give rise to new UV-dualities for which we provide evidence through an analysis of the prepotential, and which, for some examples, we substantiate by constructing the M-theory geometry in which the dual quiver descriptions are manifest.
We propose graphs, the Combined Fiber Diagrams (CFD), to characterize all 5d superconformal field theories (SCFTs) that arise as S1-reductions of 6d SCFTs. Transitions between CFDs encode mass ...deformations that trigger RG-flows between SCFTs. They provide a combinatorial classification of all such 5d SCFTs and encode physical information about the strongly coupled theories, like the superconformal flavor symmetry and BPS states. We consistently reproduce known results, but more importantly predict new theories and strong coupling effects in 5d SCFTs.
Super-spin chains for 6D SCFTs Baume, Florent; Heckman, Jonathan J.; Lawrie, Craig
Nuclear physics. B,
July 2023, 2023-07-00, 2023-07-01, Volume:
992, Issue:
C
Journal Article
Peer reviewed
Open access
Nearly all 6D superconformal field theories (SCFTs) have a partial tensor branch description in terms of a generalized quiver gauge theory consisting of a long one-dimensional spine of quiver nodes ...with links given by conformal matter; a strongly coupled generalization of a bifundamental hypermultiplet. For theories obtained from M5-branes probing an ADE singularity, this was recently leveraged to extract a protected large R-charge subsector of operators, with operator mixing controlled at leading order in an inverse large R-charge expansion by an integrable spin s Heisenberg spin chain, where s is determined by the su(2)R R-symmetry representation of the conformal matter operator. In this work, we show that this same structure extends to the full superconformal algebra osp(6,2|1). In particular, we determine the corresponding Bethe ansatz equations which govern this super-spin chain, as well as distinguished subsectors which close under operator mixing. Similar considerations extend to 6D little string theories (LSTs) and 4D N=2 SCFTs with the same generalized quiver structures.
A
bstract
We study 2d chiral theories arising from 4d
N
= 4 Super-Yang Mills (SYM) with varying coupling
τ
. The 2d theory is obtained by dimensional reduction of
N
= 4 SYM on a complex curve with a ...partial topological twist that accounts for the non-constant
τ
. The resulting 2d theories can preserve (0
,n
) with
n
= 2
,
4
,
6
,
8 chiral supersymmetry, and have a natural realization in terms of strings from wrapped D3-branes in F-theory. We determine the twisted dimensional reduction, as well as the spectrum and anomaly polynomials of the resulting strings in various dimensions. We complement this by considering the dual M-theory configurations, which can either be realized in terms of M5-branes wrapped on complex surfaces, or M2-branes on curves that result in 1d supersymmetric quantum mechanics.
A
bstract
F-theory on singular elliptically fibered Calabi-Yau four-folds provides a setting to geometrically study four-dimensional
supersymmetric gauge theories, includingmatter and Yukawa ...couplings. The gauge degrees of freedom arise from the codimension 1 singular loci, the matter and Yukawa couplings are generated at enhanced singularities in higher codimension. We construct the resolution of the singular Tate form for an elliptic Calabi-Yau four-fold with an ADE type singularity in codimension 1 and study the structure of the fibers in codimension 2 and 3. We determine the fibers in higher codimension which in general are of Kodaira type along minimal singular loci, and are thus consistent with the low energy gauge-theoretic intuition. Furthermore, we provide a complementary description of the fibers in higher codimension, which will also be applicable to non-minimal singularities. The irreducible components in the fiber in codimension 2 correspond to weights of representations of the ADE gauge group. These can split further in codimension 3 in a way that is consistent with the generation of Yukawa couplings. Applying this reasoning, we then venture out to study non-minimal singularities, which occur for
A
type along codimension 3, and for
D
and
E
also in codimension 2. The fibers in this case are non-Kodaira, however some insight into these singularities can be gained by considering the splitting of fiber components along higher codimension, which are shown to be consistent with matter and Yukawa couplings for the corresponding gauge groups.
A
bstract
For SCFTs with an SU(2) R-symmetry, we determine the superconformal blocks that contribute to the four-point correlation function of a priori distinct half-BPS superconformal primaries as ...an expansion in terms of the relevant bosonic conformal blocks. This is achieved by using the superconformal Casimir equation and the superconformal Ward identity to fix the coefficients of the bosonic blocks uniquely in a dimension-independent way. In addition we find that many of the resulting coefficients are related through a web of linear transformations of the conformal data.
F‐theory and Dark Energy Heckman, Jonathan J.; Lawrie, Craig; Lin, Ling ...
Fortschritte der Physik,
October 2019, Volume:
67, Issue:
10
Journal Article
Peer reviewed
Motivated by its potential use as a starting point for solving various cosmological constant problems, we study F‐theory compactified on the warped product Rtime×S3×Y8 where Y8 is a Spin(7) manifold, ...and the S3 factor is the target space of an SU(2) Wess–Zumino–Witten (WZW) model at level N. Reduction to M‐theory exploits the abelian duality of this WZW model to an S3/ZN orbifold. In the large N limit, the untwisted sector is captured by 11D supergravity. The local dynamics of intersecting 7‐branes in the Spin(7) geometry is controlled by a Donaldson–Witten twisted gauge theory coupled to defects. At late times, the system is governed by a 1D quantum mechanics system with a ground state annihilated by two real supercharges, which in four dimensions would appear as “N=1/2 supersymmetry” on a curved background. This leads to a cancellation of zero point energies in the 4D field theory but a split mass spectrum for superpartners of order Δm4D∼MIRMUV specified by the IR and UV cutoffs of the model. This is suggestively close to the TeV scale in some scenarios. The classical 4D geometry has an intrinsic instability which can produce either a collapsing or expanding Universe, the latter providing a promising starting point for a number of cosmological scenarios. The resulting 1D quantum mechanics in the time direction also provides an appealing starting point for a more detailed study of quantum cosmology.
Motivated by its potential use as a starting point for solving various cosmological constant problems, F‐theory is studied compactified on the warped product Rtime × S3 × Y8 where Y8 is a Spin(7) manifold, and the S3 factor is the target space of an SU(2) Wess–Zumino–Witten (WZW) model at level N. Reduction to M‐theory exploits the abelian duality of this WZW model to an S3/ZN orbifold. In the large N limit, the untwisted sector is captured by 11D supergravity. The local dynamics of intersecting 7‐branes in the Spin(7) geometry is controlled by a Donaldson–Witten twisted gauge theory coupled to defects. At late times, the system is governed by a 1D quantum mechanics system with a ground state annihilated by two real supercharges, which in four dimensions would appear as “N = 1/2 supersymmetry” on a curved background. This leads to a cancellation of zero point energies in the 4D field theory but a split mass spectrum for superpartners which is suggestively close to the TeV scale in some scenarios. The classical 4D geometry has an intrinsic instability which can produce either a collapsing or expanding Universe, the latter providing a promising starting point for a number of cosmological scenarios. The resulting 1D quantum mechanics in the time direction also provides an appealing starting point for a more detailed study of quantum cosmology.
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