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1. Calabi-Yau products: graded quivers for general toric Calabi-Yaus

   https://doi.org/10.1007/JHEP02(2021)174  

   Franco, Sebastián; Hasan, Azeem (February 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract The open string sector of the topological B-model on CY ( m + 2)-folds is described by m -graded quivers with superpotentials. This correspondence generalizes the connection between CY ( m + 2)-folds and gauge theories on the worldvolume of D(5 − 2 m )-branes for m = 0 , . . . , 3 to arbitrary m . In this paper we introduce the Calabi-Yau product, a new algorithm that starting from the known quiver theories for a pair of toric CY m +2 and CY n +2 produces the quiver theory for a related CY m + n +3 . This method significantly supersedes existing ones, enabling the simple determination of quiver theories for geometries that were previously out of practical reach. 

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2. The holographic contributions to the sphere free energy

   https://doi.org/10.1007/JHEP01(2022)171  

   Binder, Damon J.; Freedman, Daniel Z.; Pufu, Silviu S.; Zan, Bernardo (January 2022, Journal of High Energy Physics)

   A bstract We study which bulk couplings contribute to the S 3 free energy F ( $$ \mathfrak{m} $$ m ) of three-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories with holographic duals, potentially deformed by boundary real-mass parameters m. In particular, we show that F ( $$ \mathfrak{m} $$ m ) is independent of a large class of bulk couplings that include non-chiral F-terms and all D-terms. On the other hand, in general, F ( $$ \mathfrak{m} $$ m ) does depend non-trivially on bulk chiral F-terms, such as prepotential interactions, and on bulk real-mass terms. These conclusions can be reached solely from properties of the AdS super-algebra, $$ \mathfrak{osp} $$ osp (2|4). We also consider massive vector multiplets in AdS, which in the dual field theory correspond to long single-trace superconformal multiplets of spin zero. We provide evidence that F ( $$ \mathfrak{m} $$ m ) is insensitive to the vector multiplet mass and to the interaction couplings between the massive vector multiplet and massless ones. In particular, this implies that F ( $$ \mathfrak{m} $$ m ) does not contain information about scaling dimensions or OPE coefficients of single-trace long scalar $$ \mathcal{N} $$ N = 2 superconformal multiplets. 

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3. Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective

   https://doi.org/10.21468/SciPostPhys.6.5.052  

   Closset, Cyril; Del Zotto, Michele; Saxena, Vivek (January 2019, SciPost Physics)

   We revisit the correspondence between Calabi-Yau (CY) threefoldisolated singularities \mathbf{X} 𝐗 and five-dimensional superconformal field theories (SCFTs), which ariseat 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/typeIIA duality. In this setup, the low-energy gauge group simply arises onstacks of coincident D6-branes wrapping 2-cycles in some ALE space oftype A_{M-1} A M − 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” giverise to different gauge theory phases, whose existence depends on theparticular (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 theCoulomb-branch prepotential of 5d \mathcal{N}=1 𝒩 = 1 gauge theories. 

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4. 8d supergravity, reconstruction of internal geometry and the Swampland

   https://doi.org/10.1007/JHEP06(2021)178  

   Hamada, Yuta; Vafa, Cumrun (June 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract We sharpen Swampland constraints on 8d supergravity theories by studying consistency conditions on worldvolume theory of 3-brane probes. Combined with a stronger form of the cobordism conjecture, this leads to the reconstruction of the compact internal geometry and implies strong restrictions on the gauge algebra and on some higher derivative terms (related to the level of the current algebra on the 1-brane). In particular we argue that 8d supergravity theories with $$ {\mathfrak{g}}_2 $$ g 2 gauge symmetry are in the Swampland. These results provide further evidence for the string lamppost principle in 8d with 16 supercharges. 

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5. COUNTABLE MODELS OF THE THEORIES OF BALDWIN–SHI HYPERGRAPHS AND THEIR REGULAR TYPES

   https://doi.org/10.1017/jsl.2019.28  

   GUNATILLEKA, DANUL K. (September 2019, The Journal of Symbolic Logic)

   Abstract We continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $$\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } \right\}$$ of countable models of the theory of a fixed Baldwin–Shi hypergraph with $$\mathfrak{M}_\beta \preccurlyeq \mathfrak{M}_\gamma $$ if and only if the dimension of $$\mathfrak{M}_\beta $$ is at most the dimension of $$\mathfrak{M}_\gamma $$ and that each countable model is isomorphic to some $$\mathfrak{M}_\beta $$ . We also study the regular types that appear in these theories and show that the dimension of a model is determined by a particular regular type. Further, drawing on a large body of work, we use these structures to give an example of a pseudofinite, ω -stable theory with a nonlocally modular regular type, answering a question of Pillay in [11]. 

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