arXiv subjects

David R. Morrison

Publications and source records attributed to David R. Morrison.

At least 73 records · Page 4Linked to original sources

arXiv2010

Quivers from Matrix Factorizations

We discuss how matrix factorizations offer a practical method of computing the quiver and associated superpotential for a hypersurface singularity. This method also yields explicit geometrical interpretations of D-branes (i.e., quiver representations) on a resolution given in terms of Grassmannians. As an example we analyze some non-toric singularities which are resolved by a single CP1 but have "length" greater than one. These examples have a much richer structure than conifolds. A picture is proposed that relates matrix factorizations in Landau-Ginzburg theories to the way that matrix factorizations are used in this paper to perform noncommutative resolutions.

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arXiv2010

On the structure of supersymmetric T3 fibrations

We formulate some precise conjectures concerning the existence and structure of supersymmetric T3 fibrations of Calabi-Yau threefolds, and describe how these conjectural fibrations would give rise to the Strominger-Yau-Zaslow version of mirror symmetry.

math.AG↗

arXiv2009

Loop operators and S-duality from curves on Riemann surfaces

We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We then show that this precisely matches Dehn's classification of homotopy classes of non-self-intersecting curves on an associated Riemann surface--the same surface which characterizes the gauge theory. Our analysis provides an explicit prediction for the action of S-duality on loop operators in these theories which we check against the known duality transformation in several examples.

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arXiv2008

Threefold Flops via Matrix Factorization

The explicit McKay correspondence, as formulated by Gonzalez-Sprinberg and Verdier, associates to each exceptional divisor in the minimal resolution of a rational double point a matrix factorization of the equation of the rational double point. We study deformations of these matrix factorizations, and show that they exist over an appropriate "partially resolved" deformation space for rational double points of types A and D. As a consequence, all simple flops of lengths 1 and 2 can be described in terms of blowups defined from matrix factorizations. We also formulate conjectures which would extend these results to rational double points of type E and simple flops of length greater than 2.

math.AG↗

arXiv2007

D-branes and Normal Functions

We explain the B-model origin of extended Picard-Fuchs equations satisfied by the D-brane superpotential on compact Calabi-Yau threefolds. Via the Abel-Jacobi map, the domainwall tension is identified with a Poincare normal function--a transversal holomorphic section of the Griffiths intermediate Jacobian. Within this formalism, we derive the extended Picard-Fuchs equation associated with the mirror of the real quintic.

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arXiv2007

Dimensional Duality

We show that string theory on a compact negatively curved manifold, preserving a U(1)^{b_1} winding symmetry, grows at least b_1 new effective dimensions as the space shrinks. The winding currents yield a "D-dual" description of a Riemann surface of genus h in terms of its 2h dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the worldsheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a b_1-torus. In particular, we present an AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.

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arXiv2006

D-branes at Singularities, Compactification, and Hypercharge

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 comment on the relevance of D-instantons to the breaking of global U(1) symmetries.

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arXiv2005

On tachyons, gauged linear sigma models, and flip transitions

We study systems of multiple localized closed string tachyons and the phenomena associated with their condensation, in C3/ZN nonsupersymmetric noncompact orbifold singularities using gauged linear sigma model constructions, following hep-th/0406039. Our study reveals close connections between the combinatorics of nonsupersymmetric flip transitions (between topologically distinct resolutions of the original singularity), the physics of tachyons of different degrees of relevance and the singularity structure of the corresponding residual endpoint geometries. This in turn can be used to study the stability of the phases of gauged linear sigma models and gain qualitative insight into the closed string tachyon potential.

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arXiv2004

TASI Lectures on Compatification and Duality

We describe the moduli spaces of theories with 32 or 16 supercharges, from several points of view. Included is a review of backgrounds with D-branes (including type I' vacua and F-theory), a discussion of holonomy of Riemannian metrics, and an introduction to the relevant portions of algebraic geometry. The case of K3 surfaces is treated in some detail.

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arXiv2004

Localized tachyons in C^3/Z_N

We study the condensation of localized closed string tachyons in C^3/Z_N nonsupersymmetric noncompact orbifold singularities via renormalization group flows that preserve supersymmetry in the worldsheet conformal field theory and their interrelations with the toric geometry of these orbifolds. We show that for worldsheet supersymmetric tachyons, the endpoint of tachyon condensation generically includes ``geometric'' terminal singularities (orbifolds that do not have any marginal or relevant Kahler blowup modes) as well as singularities in codimension two. Some of the various possible distinct geometric resolutions are related by flip transitions. For Type II theories, we show that the residual singularities that arise under tachyon condensation in various classes of Type II theories also admit a Type II GSO projection. We further show that Type II orbifolds entirely devoid of marginal or relevant blowup modes (Kahler or otherwise) cannot exist, which thus implies that the endpoints of tachyon condensation in Type II theories are always smooth spaces.

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arXiv2003

Triples, Fluxes, and Strings

We study string compactifications with sixteen supersymmetries. The moduli space for these compactifications becomes quite intricate in lower dimensions, partly because there are many different irreducible components. We focus primarily, but not exclusively, on compactifications to seven or more dimensions. These vacua can be realized in a number ways: the perturbative constructions we study include toroidal compactifications of the heterotic/type I strings, asymmetric orbifolds, and orientifolds. In addition, we describe less conventional M and F theory compactifications on smooth spaces. The last class of vacua considered are compactifications on singular spaces with non-trivial discrete fluxes. We find a number of new components in the string moduli space. Contained in some of these components are M theory compactifications with novel kinds of ``frozen'' singularities. We are naturally led to conjecture the existence of new dualities relating spaces with different singular geometries and fluxes. As our study of these vacua unfolds, we also learn about additional topics including: F theory on spaces without section, automorphisms of del Pezzo surfaces, and novel physics (and puzzles) from equivariant K-theory. Lastly, we comment on how the data we gain about the M theory three-form might be interpreted.

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arXiv2001

Novel Type I Compactifications

We argue that there are two distinct classes of type I compactification to four dimensions on any space. These two classes are distinguished in a mysterious way by the presence (or absence) of a discrete 6-form potential. In simple examples, duality suggests that the new class of compactifications have reduced numbers of moduli. We also point out analogous discrete choices in M, F and type II compactifications, including some with $G_2$ holonomy. These choices often result in spaces with frozen singularities.

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arXiv2000

Codimension-Three Bundle Singularities in F-Theory

We study new nonperturbative phenomena in N=1 heterotic string vacua corresponding to pointlike bundle singularities in codimension three. These degenerations result in new four-dimensional infrared physics characterized by light solitonic states whose origin is explained in the dual F-theory model. We also show that such phenomena appear generically in $E_7 \to E_6$ Higgsing and describe in detail the corresponding bundle transition.

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arXiv2000

Geometric Aspects of Mirror Symmetry

The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X,Y) of Calabi-Yau threefolds, the best-understood mirror statements relate certain small corners of the moduli spaces of X and of Y. We will indicate how one might go beyond such statements, and relate the moduli spaces more globally. In fact, in the boldest version of mirror symmetry (the Strominger-Yau-Zaslow conjecture), the Calabi-Yau threefolds X and Y should be directly related to each other through a very geometric construction.

math.AG↗

arXiv2000

Lie Groups, Calabi-Yau Threefolds, and F-Theory

The F-theory vacuum constructed from an elliptic Calabi-Yau threefold with section yields an effective six-dimensional theory. The Lie algebra of the gauge sector of this theory and its representation on the space of massless hypermultiplets are shown to be determined by the intersection theory of the homology of the Calabi-Yau threefold. (Similar statements hold for M-theory and the type IIA string compactified on the threefold, where there is also a dependence on the expectation values of the Ramond-Ramond fields.) We describe general rules for computing the hypermultiplet spectrum of any F-theory vacuum, including vacua with non-simply-laced gauge groups. The case of monodromy acting on a curve of A_even singularities is shown to be particularly interesting and leads to some unexpected rules for how 2-branes are allowed to wrap certain 2-cycles. We also review the peculiar numerical predictions for the geometry of elliptic Calabi-Yau threefolds with section which arise from anomaly cancellation in six dimensions.

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arXiv2000

Group representations and the Euler characteristic of elliptically fibered Calabi-Yau threefolds

To every elliptic Calabi-Yau threefold with a section $X$ there can be associated a Lie group $G$ and a representation $ρ$ of that group. The group is determined from the Weierstrass model, which has singularities that are generically rational double points; these double points lead to local factors of $G$ which are either the corresponding A-D-E groups or some associated non-simply laced groups. The representation $ρ$ is a sum of representations coming from the local factors of $G$, and of other representations which can be associated to the points at which the singularities are worse than generic. This construction first arose in physics, and the requirement of anomaly cancellation in the associated physical theory makes some surprising predictions about the connection between $X$ and $ρ$. In particular, an explicit formula (in terms of $ρ$) for the Euler characteristic of $X$ is predicted. We give a purely mathematical proof of that formula in this paper, introducing along the way a new invariant of elliptic Calabi-Yau threefolds. We also verify the other geometric predictions which are consequences of anomaly cancellation, under some (mild) hypotheses about the types of singularities which occur. As a byproduct we also discover a novel relation between the Coxeter number and the rank in the case of the simply laced groups in the ``exceptional series'' studied by Deligne.

math.AG↗

arXiv1998

Non-Spherical Horizons, I

We formulate an extension of Maldacena's AdS/CFT conjectures to the case of branes located at singular points in the ambient transverse space. For singularities which occur at finite distance in the moduli space of M or F theory models with spacetime-filling branes, the conjectures identify the worldvolume theory on the p-branes with a compactification of M or IIB theory on $AdS_{p+2} \times H^{D-p-2}$. We show how the singularity determines the horizon H, and demonstrate the relationship between global symmetries on the worldvolume and gauge symmetries in the AdS model. As a first application, we study some singularities relevant to the D3-branes required in four-dimensional F-theory. For these we are able to explicitly derive the low-energy field theory on the worldvolume and compare its properties to predictions from the dual AdS model. In particular, we examine the baryon spectra of the models and the fate of the Abelian factors in the gauge group.

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arXiv1998

Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves

We consider the F-theory description of non-simply-connected gauge groups appearing in the E8 x E8 heterotic string. The analysis is closely tied to the arithmetic of torsion points on an elliptic curve. The general form of the corresponding elliptic fibration is given for all finite subgroups of E8 which are applicable in this context. We also study the closely-related question of point-like instantons on a K3 surface whose holonomy is a finite group. As an example we consider the case of the heterotic string on a K3 surface having the E8 gauge symmetry broken to (E6 x SU(3))/Z3 or SU(9)/Z3 by point-like instantons with Z3 holonomy.

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