1-form symmetry, isolated $$ \mathcal{N} $$ = 2 SCFTs, and Calabi-Yau threefolds

We systematically study 4D $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in ℂ4. We show that if a theory in this class has no $$ \mathcal{N} $$ N = 2-preserving exactly marginal deformation (i.e., the theory is isolated as an $$ \mathcal{N} $$ N = 2 SCFT), then it has no 1-form symmetry. This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the a and c central charges, this condition implies that IHS theories satisfying $$ a<\frac{1}{24}\left(15r+2f\right) $$ a < 1 24 15 r + 2 f and $$ c<\frac{1}{6}\left(3r+f\right) $$ c < 1 6 3 r + f (where r is the complex dimension of the Coulomb branch, and f is the rank of the continuous 0-form flavor symmetry) have no 1-form symmetry. After reviewing the 1-form symmetries of other classes of theories, we are motivated to conjecture that general interacting 4D $$ \mathcal{N} $$ N = 2 SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.

Connecting 5d Higgs branches via Fayet-Iliopoulos deformations

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.

Finding AdS5 × S5 in 2+1 dimensional SCFT physics

We study solutions of type IIB string theory dual to $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory on half of ℝ3,1 coupled to holographic three-dimensional superconformal field theories (SCFTs) at the edge of this half-space. The dual geometries are asymptotically AdS5×S5 with boundary geometry ℝ2,1×ℝ+, with a geometrical end-of-the-world (ETW) brane cutting off the other half of the asymptotic region of the would-be Poincaré AdS5×S5. We show that by choosing the 3D SCFT appropriately, this ETW brane can be pushed arbitrarily far towards the missing asymptotic region, recovering the “missing” half of Poincaré AdS5×S5. We also show that there are 3D SCFTs whose dual includes a wedge of Poincaré AdS5×S5 with an angle arbitrarily close to π, with geometrical ETW branes on either side.

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

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.

A CFT distance conjecture

We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

Superconformal Line Defects in 3D

We review the recent progress in the study of line defects in three-dimensional Chern–Simons-matter superconformal field theories, notably the ABJM theory. The first part is focused on kinematical defects, supporting a topological sector of the theory. After reviewing the construction of this sector, we concentrate on the evaluation of topological correlators from the partition function of the mass-deformed ABJM theory and provide evidence on the existence of topological quantum mechanics living on the line. In the second part, we consider the dynamical defects realized as latitude BPS Wilson loops for which an exact evaluation is available in terms of a latitude Matrix Model. We discuss the fundamental relation between these operators, the defect superconformal field theory and bulk physical quantities, such as the Bremsstrahlung function. This relation assigns a privileged role to BPS Wilson operators, which become the meeting point for three exact approaches: localization, integrability and conformal bootstrap.

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

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.

Supersymmetric Janus solutions in $$\omega $$-deformed $$N=8$$ gauged supergravity

We give a large class of supersymmetric Janus solutions in $$\omega $$ ω -deformed (dyonic) SO(8) maximal gauged supergravity with $$\omega =\frac{\pi }{8}$$ ω = π 8 . Unlike the purely electric counterpart, the dyonic SO(8) gauged supergravity exhibits a richer structure of $$AdS_4$$ A d S 4 vacua with $$N=8,2,1,1$$ N = 8 , 2 , 1 , 1 supersymmetries and SO(8), U(3), $$G_2$$ G 2 and SU(3) symmetries, respectively. Similarly, domain walls interpolating among these critical points show a very rich structure as well. In this paper, we show that this gauged supergravity also accommodates a number of interesting supersymmetric Janus solutions in the form of $$AdS_3$$ A d S 3 -sliced domain walls asymptotically interpolating between the aforementioned $$AdS_4$$ A d S 4 geometries. These solutions could be holographically interpreted as two-dimensional conformal defects within the superconformal field theories (SCFTs) of ABJM type dual to the $$AdS_4$$ A d S 4 vacua. We also give a class of solutions interpolating among the SO(8), $$G_2$$ G 2 and U(3) $$AdS_4$$ A d S 4 vacua in the case of $$\omega =0$$ ω = 0 which have not previously appeared in the presently known Janus solutions of electric SO(8) gauged supergravity.

T $$ \overline{T} $$ deformation in SCFTs and integrable supersymmetric theories

We calculate the $$ \mathcal{S} $$ S -multiplets for two-dimensional Euclidean $$ \mathcal{N} $$ N = (0, 2) and $$ \mathcal{N} $$ N = (2, 2) superconformal field theories under the T$$ \overline{T} $$ T ¯ deformation at leading order of perturbation theory in the deformation coupling. Then, from these $$ \mathcal{N} $$ N = (0, 2) deformed multiplets, we calculate two- and three-point correlators. We show the $$ \mathcal{N} $$ N = (0, 2) chiral ring’s elements do not flow under the T$$ \overline{T} $$ T ¯ deformation. Specializing to integrable supersymmetric seed theories, such as $$ \mathcal{N} $$ N = (2, 2) Landau-Ginzburg models, we use the thermodynamic Bethe ansatz to study the S-matrices and ground state energies. From both an S-matrix perspective and Melzer’s folding prescription, we show that the deformed ground state energy obeys the inviscid Burgers’ equation. Finally, we show that several indices independent of D-term perturbations including the Witten index, Cecotti-Fendley-Intriligator-Vafa index and elliptic genus do not flow under the T$$ \overline{T} $$ T ¯ deformation.

Compactifying 5d superconformal field theories to 3d

Building on recent progress in the study of compactifications of 6d (1, 0) superconformal field theories (SCFTs) on Riemann surfaces to 4d$$ \mathcal{N} $$ N = 1 theories, we initiate a systematic study of compactifications of 5d$$ \mathcal{N} $$ N = 1 SCFTs on Riemann surfaces to 3d$$ \mathcal{N} $$ N = 2 theories. Specifically, we consider the compactification of the so-called rank 1 Seiberg $$ {E}_{N_f+1} $$ E N f + 1 SCFTs on tori and tubes with flux in their global symmetry, and put the resulting 3d theories to various consistency checks. These include matching the (usually enhanced) IR symmetry of the 3d theories with the one expected from the compactification, given by the commutant of the flux in the global symmetry of the corresponding 5d SCFT, and identifying the spectrum of operators and conformal manifolds predicted by the 5d picture. As the models we examine are in three dimensions, we encounter novel elements that are not present in compactifications to four dimensions, notably Chern-Simons terms and monopole superpotentials, that play an important role in our construction. The methods used in this paper can also be used for the compactification of any other 5d SCFT that has a deformation leading to a 5d gauge theory.