arXiv subjects

Ilarion V. Melnikov

Publications and source records attributed to Ilarion V. Melnikov.

At least 37 records · Page 2Linked to original sources

arXiv2016

Relevant deformations and c-extremization

We consider RG flows obtained by a relevant deformation from unitary and compact two-dimensional (0,2) SCFTs. We point out that an N=2 super-Kac-Moody algebra present in the UV is preserved by the flow and does not mix with the R-current. On the other hand, a direct sum of N=2 algebras in the UV theory leads to a few complications in determining the IR R-symmetry; nevertheless, in flows without accidental IR symmetries, we determine the IR R-symmetry and show that it maximizes the IR central charge.

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arXiv2016

Some tree-level string amplitudes in the NSR formalism

We calculate tree level scattering amplitudes for open strings using the NSR formalism. We present a streamlined symmetry-based and pedagogical approach to the computations, which we first develop by checking two-, three-, and four-point functions involving bosons and fermions. We calculate the five-point amplitude for massless gluons and find agreement with an earlier result by Brandt, Machado and Medina. We then compute the five-point amplitudes involving two and four fermions respectively, the general form of which has not been previously obtained in the NSR formalism. The results nicely confirm expectations from the supersymmetric $F^4$ effective action. Finally we use the prescription of Kawai, Lewellen and Tye (KLT) to compute the amplitudes for the closed string sector.

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arXiv2016

UV Completions for Non-Critical Strings

Compactifications of the physical superstring to two dimensions provide a general template for realizing 2D conformal field theories coupled to worldsheet gravity, i.e. non-critical string theories. Motivated by this observation, in this paper we determine the quasi-topological 8D theory which governs the vacua of 2D N = (0,2) gauged linear sigma models (GLSMs) obtained from compactifications of type I and heterotic strings on a Calabi-Yau fourfold. We also determine the quasi-topological 6D theory governing the 2D vacua of intersecting 7-branes in compactifications of F-theory on an elliptically fibered Calabi-Yau fivefold, where matter fields and interaction terms localize on lower-dimensional subspaces, i.e. defect operators. To cancel anomalies / cancel tadpoles, these GLSMs must couple to additional chiral sectors, which in some cases do not admit a known description in terms of a UV GLSM. Additionally, we find that constructing an anomaly free spectrum can sometimes break supersymmetry due to spacetime filling anti-branes. We also study various canonical examples such as the standard embedding of heterotic strings on a Calabi-Yau fourfold and F-theoretic "rigid clusters" with no local deformation moduli of the elliptic fibration.

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arXiv2014

Accidents in (0,2) Landau-Ginzburg theories

We study the role of accidental symmetries in two-dimensional (0,2) superconformal field theories obtained by RG flow from (0,2) Landau-Ginzburg theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) Landau-Ginzburg models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. We also give a self-contained discussion of aspects of (0,2) conformal perturbation theory.

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arXiv2014

Global aspects of (0,2) moduli space: toric varieties and tangent bundles

We study the moduli space of A/2 half-twisted gauged linear sigma models for NEF Fano toric varieties. Focusing on toric deformations of the tangent bundle, we describe the vacuum structure of many (0,2) theories, in particular identifying loci in parameter space with spontaneous supersymmetry breaking or divergent ground ring correlators. We find that the parameter space of such an A/2 theory and its ground ring is in general a moduli stack, and we show in examples that with suitable stability conditions it is possible to obtain a simple compactification of the moduli space of smooth A/2 theories.

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arXiv2014

Heterotic fluxes and supersymmetry

We show that the formal alpha' expansion for heterotic flux vacua is only sensible when flux quantization and the appearance of string scale cycles in the geometry are carefully taken into account. We summarize a number of properties of solutions with N=1 and N=2 space-time supersymmetry.

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arXiv2014

Massless spectrum for hybrids CFTs

We describe a class of theories obtained by fibering a Landau-Ginburg orbifold over a compact Kaehler base. While such theories are often described as phases of some GLSM, our description is independent of such an embedding. We provide a method for computing the massless spectrum. This note is based on the longer paper arXiv:1307.7063.

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arXiv2013

Global Symmetries and N=2 SUSY

We prove that N=2 theories that arise by taking n free hypermultiplets and gauging a subgroup of Sp(n), the non-R global symmetry of the free theory, have a remaining global symmetry which is a direct sum of unitary, symplectic, and special orthogonal factors. This implies that theories that have SU(N) but not U(N) global symmetries, such as Gaiotto's T_N theories, are not likely to arise as IR fixed points of RG flows from weakly coupled N=2 gauge theories.

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arXiv2013

Hybrid conformal field theories

We describe a class of (2,2) superconformal field theories obtained by fibering a Landau-Ginzburg orbifold CFT over a compact Kaehler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model, our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of linear models and comparing spectra among the phases.

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arXiv2013

Target Spaces from Chiral Gauge Theories

Chiral gauge theories in two dimensions with (0,2) supersymmetry are central in the study of string compactifications. Remarkably little is known about generic (0,2) theories. We consider theories with branches on which multiplets with a net gauge anomaly become massive. The simplest example is a relevant perturbation of the gauge theory that flows to the CP(n) model. To compute the effective action, we derive a useful set of Feynman rules for (0,2) supergraphs. From the effective action, we see that the infra-red geometry reflects the gauge anomaly by the presence of a boundary at finite distance. In generic examples, there are boundaries, fluxes and branes; the resulting spaces are non-Kahler.

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arXiv2012

Recent Developments in (0,2) Mirror Symmetry

Mirror symmetry of the type II string has a beautiful generalization to the heterotic string. This generalization, known as (0,2) mirror symmetry, is a field still largely in its infancy. We describe recent developments including the ideas behind quantum sheaf cohomology, the mirror map for deformations of (2,2) mirrors, the construction of mirror pairs from worldsheet duality, as well as an overview of some of the many open questions. The (0,2) mirrors of Hirzebruch surfaces are presented as a new example.

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arXiv2012

Heterotic Sigma Models with N=2 Space-Time Supersymmetry

We study the non-linear sigma model realization of a heterotic vacuum with N=2 space-time supersymmetry. We examine the requirements of (0,2) + (0,4) world-sheet supersymmetry and show that a geometric vacuum must be described by a principal two-torus bundle over a K3 manifold.

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arXiv2011

On marginal deformations of (0,2) non-linear sigma models

An N=1, d=4 supersymmetric compactification of the perturbative heterotic string is described by a d=2 (0,2) superconformal field theory. The first-order marginal deformations of the internal (0,2) SCFT are in 1 to 1 correspondence with massless gauge-neutral scalars in the spacetime theory. Working at tree-level in the alpha' expansion, we describe these first order deformations for SCFTs with a (0,2) non-linear sigma model description. Our results clarify the structure of deformations of heterotic Calabi-Yau compactifications and more general heterotic flux vacua.

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arXiv2011

Old issues and linear sigma models

Using mirror symmetry, we resolve an old puzzle in the linear sigma model description of the spacetime Higgs mechanism in a heterotic string compactification with (2,2) worldsheet supersymmetry. The resolution has a nice spacetime interpretation via the normalization of physical fields and suggests that with a little care deformations of the linear sigma model can describe heterotic Higgs branches.

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arXiv2010

(0,2) Elephants

We enumerate massless E6 singlets for (0,2)-compactifications of the heterotic string on a Calabi-Yau threefold with the "standard embedding" in three distinct ways. In the large radius limit of the threefold, these singlets count deformations of the Calabi-Yau together with its tangent bundle. In the "small-radius" limit we apply Landau-Ginzburg methods. In the orbifold limit we use a combination of geometry and free field methods. In general these counts differ. We show how to identify states between these phases and how certain states vanish from the massless spectrum as one deforms the complex structure or Kaehler form away from the Gepner point. The appearance of extra singlets for particular values of complex structure is explored in all three pictures, and our results suggest that this does not depend on the Kaehler moduli.

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arXiv2010

A (0,2) Mirror Map

We study the linear sigma model subspace of the moduli space of (0,2) superconformal world-sheet theories obtained by deforming (2,2) theories based on Calabi-Yau hypersurfaces in reflexively plain toric varieties. We describe a set of algebraic coordinates on this subspace, formulate a (0,2) generalization of the monomial-divisor mirror map, and show that the map exchanges principal components of singular loci of the mirror half-twisted theories. In non-reflexively plain examples the proposed map yields a mirror isomorphism between subfamilies of linear sigma models.

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arXiv2010

(0,2) Deformations of Linear Sigma Models

We study (0,2) deformations of a (2,2) supersymmetric gauged linear sigma model for a Calabi-Yau hypersurface in a Fano toric variety. In the non-linear sigma model these correspond to some of the holomorphic deformations of the tangent bundle on the hypersurface. Combinatorial formulas are given for the number of these deformations, and we show that these numbers are exchanged by mirror symmetry in a subclass of the models.

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arXiv2010

Summing the Instantons in Half-Twisted Linear Sigma Models

We study half-twisted linear sigma models relevant to (0,2) compactifications of the heterotic string. Focusing on theories with a (2,2) locus, we examine the linear model parameter space and the dependence of genus zero half-twisted correlators on these parameters. We show that in a class of theories the correlators and parameters separate into A and B types, present techniques to compute the dependence, and apply these to some examples. These results should bear on the mathematics of (0,2) mirror symmetry and the physics of the moduli space and Yukawa couplings in heterotic compactifications.

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