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We report on progress towards the construction of SM- like gauge theories on the world-volume of D-branes at a Calabi-Yau singularity. In particular, we work out the topological conditions on the embedding of the singularity inside a compact CY threefold, that select hypercharge as the only light U(1) gauge factor. We apply this insight to the proposed open string realization of the SM of hep-th/0508089, based on a D3-brane at a dP(8) singularity, and present a geometric construction of a compact Calabi-Yau threefold with all the required topological properties.

We systematically study 4D 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 N = 2-preserving exactly marginal deformation (i.e., the theory is isolated as an 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 < 1 24 15 r + 2 f and 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 N = 2 SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry. [ABSTRACT FROM AUTHOR]

Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), $$ {\mathcal{T}}_{3,\frac{3}{2}} $$ , emerging in this duality splits into a free piece and an interacting piece, $$ {\mathcal{T}}_X $$ , even though this factorization seems invisible in the Seiberg-Witten (SW) curve derived from the corresponding M5-brane construction. Without a Lagrangian, an associated topological field theory, a BPS spectrum, or even an SW curve, we nonetheless obtain exact information about $$ {\mathcal{T}}_X $$ by bootstrapping its chiral algebra, $$ {}_{\mathcal{X}}\left({\mathcal{T}}_X\right) $$ , and finding the corresponding vacuum character in terms of Affine Kac-Moody characters. By a standard 4D/2D correspondence, this result gives us the Schur index for $$ {\mathcal{T}}_X $$ and, by studying this quantity in the limit of small S , we make contact with a proposed S reduction. Along the way, we discuss various properties of $$ {\mathcal{T}}_X $$ : as an $$ \mathcal{N} $$ = 1 theory, it has flavor symmetry SU(3) × SU(2) × U(1), the central charge of $$ {}_{\mathcal{X}}\left({\mathcal{T}}_X\right) $$ matches the central charge of the bc ghosts in bosonic string theory, and its global SU(2) symmetry has a Witten anomaly. This anomaly does not prevent us from building conformal manifolds out of arbitrary numbers of $$ {\mathcal{T}}_X $$ theories (giving us a surprisingly close AD relative of Gaiotto's T theories), but it does lead to some open questions in the context of the chiral algebra/4D $$ \mathcal{N} $$ =2SCFT correspondence. [ABSTRACT FROM AUTHOR]

In this note, we study a large class of four-dimensional R-symmetric theories, and we describe a new quantity TU which is well defined in these theories. Furthermore, we conjecture that this quantity is larger in the ultraviolet (UV) than in the infrared (IR), i.e., that TUVU > TIRU. While we do not prove this inequality in full generality, it is straightforward to show that our conjecture holds in the subset of theories that do not have accidental symmetries. In addition, we subject our inequality to an array of nontrivial tests in theories with accidental symmetries and dramatically different dynamics both in N = 1 and N = 2 supersym-metry and find that our inequality is obeyed. One interesting consequence of this conjecture is that the mixing of accidental symmetries with the IR superconformai R current is bounded by the UV quantity, TUVU. To demonstrate the potential utility of this bound, we apply it to the somewhat mysterious SU(2) gauge theory of Intriligator, Seiberg, and Shenker and show that our conjecture, if correct, implies that this theory flows in the IR to an interacting superconformai field theory. [ABSTRACT FROM AUTHOR]