# Browsing by Subject "hep-th"

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Item Open Access A (0,2) mirror dualityBertolini, Marco; Plesser, M RonenWe construct a class of exactly solved (0,2) heterotic compactifications, similar to the (2,2) models constructed by Gepner. We identify these as special points in moduli spaces containing geometric limits described by non-linear sigma models on complete intersection Calabi-Yau spaces in toric varieties, equipped with a bundle whose rank is strictly greater than that of the tangent bundle. These moduli spaces do not in general contain a locus exhibiting (2,2) supersymmetry. A quotient procedure at the exactly solved point realizes the mirror isomorphism, as was the case for Gepner models. We find a geometric interpretation of the mirror duality in the context of hybrid models.Item Metadata only A nontrivial critical fixed point for replica-symmetry-breaking transitions(2017-04-01) Charbonneau, Patrick; Yaida, ShoThe transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon--the Gardner transition--has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, d_u=6. Here, we obtain evidence for the existence of these transitions in dItem Open Access Coarse-graining quiversNarayan, K; Plesser, M RonenWe describe a block-spin-like transformation on a simplified subset of the space of supersymmetric quiver gauge theories that arise on the worldvolumes of D-brane probes of orbifold geometries, by sequentially Higgsing the gauge symmetry in these theories. This process flows to lower worldvolume energies in the regions of the orbifold moduli space where the closed string blowup modes, and therefore the expectation values of the bifundamental scalars, exhibit a hierarchy of scales. Lifting to the ``upstairs'' matrices of the image branes makes contact with the matrix coarse-graining defined in a previous paper. We describe the structure of flows we observe under this process. The quiver lattice for $\BC^2/\BZ_N$ in this region of moduli space deconstructs an inhomogeneous, fractal-like extra dimension, in terms of which our construction describes a coarse-graining of the deconstruction lattice.Item Open Access Counting Yang-Mills Dyons with Index Theorems(Phys.Rev. D, 2017-06-01) Stern, M; Yi, PWe count the supersymmetric bound states of many distinct BPS monopoles in N=4 Yang-Mills theories and in pure N=2 Yang-Mills theories. The novelty here is that we work in generic Coulombic vacua where more than one adjoint Higgs fields are turned on. The number of purely magnetic bound states is again found to be consistent with the electromagnetic duality of the N=4 SU(n) theory, as expected. We also count dyons of generic electric charges, which correspond to 1/4 BPS dyons in N=4 theories and 1/2 BPS dyons in N=2 theories. Surprisingly, the degeneracy of dyons is typically much larger than would be accounted for by a single supermultiplet of appropriate angular momentum, implying many supermutiplets of the same charge and the same mass.Item Open Access From vortices to instantons on the Euclidean Schwarzschild manifold(2018-01-18) Nagy, Ákos; Oliveira, GonçaloThe first irreducible solution of the $\SU (2)$ self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later than the famous BPST instantons on $\rl^4$ were discovered. While soon after, in 1978, the ADHM construction gave a complete description of the moduli spaces of instantons on $\rl^4$, the case of the Euclidean Schwarzschild manifold has resisted many efforts for the past 40 years. By exploring a correspondence between the planar Abelian vortices and spherically symmetric instantons on ES, we obtain: a complete description of a connected component of the moduli space of unit energy $\SU (2)$ instantons; new examples of instantons with non-integer energy (and non-trivial holonomy at infinity); a complete classification of finite energy, spherically symmetric, $\SU (2)$ instantons. As opposed to the previously known solutions, the generic instanton coming from our construction is not invariant under the full isometry group, in particular not static. Hence disproving a conjecture of Tekin.Item Open Access Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomialsEkholm, Tobias; Ng, LenhardWe sketch a construction of Legendrian Symplectic Field Theory (SFT) for conormal tori of knots and links. Using large $N$ duality and Witten's connection between open Gromov-Witten invariants and Chern-Simons gauge theory, we relate the SFT of a link conormal to the colored HOMFLY-PT polynomials of the link. We present an argument that the HOMFLY-PT wave function is determined from SFT by induction on Euler characteristic, and also show how to, more directly, extract its recursion relation by elimination theory applied to finitely many noncommutative equations. The latter can be viewed as the higher genus counterpart of the relation between the augmentation variety and Gromov-Witten disk potentials established by Aganagic, Vafa, and the authors, and, from this perspective, our results can be seen as an SFT approach to quantizing the augmentation variety.Item Open Access Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem(Journal of Differential Geometry, 2019-12-06) Cherkis, Sergey A; Larrain-Hubach, Andres; Stern, MarkWe study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series of papers proving the completeness of the bow construction of instantons on multi-Taub-NUT spaces and exploring it in detail.Item Open Access Instantons on multi-Taub-NUT Spaces II: Bow ConstructionCherkis, Sergey; Larraín-Hubach, Andrés; Stern, MarkUnitary anti-self-dual connections on Asymptotically Locally Flat (ALF) hyperk\"ahler spaces are constructed in terms of data organized in a bow. Bows generalize quivers, and the relevant bow gives rise to the underlying ALF space as the moduli space of its particular representation -- the small representation. Any other representation of that bow gives rise to anti-self-dual connections on that ALF space. We prove that each resulting connection has finite action, i.e. it is an instanton. Moreover, we derive the asymptotic form of such a connection and compute its topological class.Item Open Access Invariance Theorems for Supersymmetric Yang-Mills Theories(Adv.Theor.Math.Phys., 2017-06-01) Sethi, S; Stern, MWe consider quantum mechanical Yang-Mills theories with eight supercharges and a $Spin(5) \times SU(2)_R$ flavor symmetry. We show that all normalizable ground states in these gauge theories are invariant under this flavor symmetry. This includes, as a special case, all bound states of D0-branes and D4-branes. As a consequence, all bound states of D0-branes are invariant under the $Spin(9)$ flavor symmetry. When combined with index results, this implies that the bound state of two D0-branes is unique.Item Open Access Mirror Symmetry and DiscriminantsAspinwall, Paul S; Plesser, M Ronen; Wang, KangkangWe analyze the locus, together with multiplicities, of "bad" conformal field theories in the compactified moduli space of N=(2,2) superconformal field theories in the context of the generalization of the Batyrev mirror construction using the gauged linear sigma-model. We find this discriminant of singular theories is described beautifully by the GKZ "A-determinant" but only if we use a noncompact toric Calabi-Yau variety on the A-model side and logarithmic coordinates on the B-model side. The two are related by "local" mirror symmetry. The corresponding statement for the compact case requires changing multiplicities in the GKZ determinant. We then describe a natural structure for monodromies around components of this discriminant in terms of spherical functors. This can be considered a categorification of the GKZ A-determinant. Each component of the discriminant is naturally associated with a category of massless D-branes.Item Open Access New G2-holonomy cones and exotic nearly Kahler structures on S^{6}and S^{3}x S^{3}(Annals of Mathematics, 2017-01-01) Foscolo, L; Haskins, M© 2017 Department of Mathematics, Princeton University. There is a rich theory of so-called (strict) nearly Kahler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kahler 6-manifolds play a distinguished role both in the general structure theory and also because of their connection with singular spaces with holonomy group the compact exceptional Lie group G2: The metric cone over a Riemannian 6-manifold M has holonomy contained in G2 if and only if M is a nearly Kahler 6-manifold. A central problem in the field has been the absence of any complete inhomogeneous examples. We prove the existence of the first complete inhomogeneous nearly Kahler 6-manifolds by proving the existence of at least one cohomogeneity one nearly Kahler structure on the 6-sphere and on the product of a pair of 3-spheres. We conjecture that these are the only simply connected (inhomogeneous) cohomogeneity one nearly Kahler structures in six dimensions.