Tony Pantev

The Exact MSSM spectrum from string theory

We show the existence of realistic vacua in string theory whose observable sector has exactly the matter content of the MSSM. This is achieved by compactifying the E_8 x E_8 heterotic superstring on a smooth Calabi-Yau threefold with an SU(4) gauge instanton and a Z_3 x Z_3 Wilson line. Specifically, the observable sector is N=1 supersymmetric with gauge group SU(3)_C x SU(2)_L x U(1)_Y x U(1)_{B-L}, three families of quarks and leptons, each family with a right-handed neutrino, and one Higgs-Higgs conjugate pair. Importantly, there are no extra vector-like pairs and no exotic matter in the zero mode spectrum. There are, in addition, 6 geometric moduli and 13 gauge instanton moduli in the observable sector. The holomorphic SU(4) vector bundle of the observable sector is slope-stable.

Standard-model bundles on non-simply connected Calabi-Yau threefolds

We give a proof of the existence of G = SU(5), stable holomorphic vector bundles on elliptically bered Calabi-Yau threefolds with fundamental group Z2. ThebundlesweconstructhaveEulercharacteristic3andananomalythatcanbe absorbed by M-theory ve-branes. Such bundles provide the basis for constructing the standard model in heterotic M-theory. They are also applicable to vacua of the weakly coupled heterotic string. We explicitly present a class of three family models with gauge group SU(3)CSU(2)LU(1)Y.

Non-Birational Twisted Derived Equivalences in Abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kähler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kähler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov’s ‘homological projective duality.’ Along the way, we shall see how ‘noncommutative spaces’ (in Kontsevich’s sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.

SU(4) instantons on Calabi-Yau threefolds with Z(2) x Z(2) fundamental group

Structure group SU(4) gauge vacua of both weakly and strongly coupled heterotic superstring theory compactified on torus-fibered Calabi-Yau threefolds Z with 2 × 2 fundamental group are presented. This is accomplished by constructing invariant, stable, holomorphic rank four vector bundles on the simply connected cover of Z. Such bundles can descend either to Hermite-Yang-Mills instantons on Z or to twisted gauge fields satisfying the Hermite-Yang-Mills equation corrected by a non-trivial flat B-field. It is shown that large families of such instantons satisfy the constraints imposed by particle physics phenomenology. The discrete parameter spaces of those families are presented, as well as a lower bound on the dimension of the continuous moduli of any such vacuum. In conjunction with 2 × 2 Wilson lines, these SU(4) gauge vacua can lead to standard-like models at low energy with an additional U(1)B−L symmetry. This U(1)B−L symmetry is very helpful in naturally suppressing nucleon decay.

Cluster decomposition, T-duality, and gerby CFTs

In this paper we study CFT’s associated to gerbes. These theories suffer from a lack of cluster decomposition, but this problem can be resolved: the CFT’s are the same as CFT’s for disconnected targets. Such theories also lack cluster decomposition, but in that form, the lack is manifestly not very problematic. In particular, we shall see that this matching of CFT’s, this duality between noneffective-gaugings and sigma models on disconnected targets, is a worldsheet duality related to T-duality. We perform a wide variety of tests of this claim, ranging from checking partition functions at arbitrary genus to D-branes to mirror symmetry. We also discuss a number of applications of these results, including predictions for quantum cohomology and Gromov-Witten theory and additional physical understanding of the geometric Langlands program.

Torus fibrations, gerbes, and duality

Introduction The Brauer group and the Tate-Shafarevich group Smooth genus one fibrations Surfaces Modified

Elliptic Calabi-Yau Threefolds with Z_3 x Z_3 Wilson Lines

T

GLSMs for gerbes (and other toric stacks)

-duality and the SYZ conjecture Appendix A. Duality for representations of

Torus-Fibered Calabi-Yau threefolds with non-trivial fundamental group

1

Shifted Poisson structures and deformation quantization

-motives, by Dmitry Arinkin Bibliography.