On the Chiral Ring of N=1 Supersymmetric Gauge Theories

We consider the chiral ring of the pure N=1 supersymmetric gauge theory with SU(N) gauge group and show that the classical relation S^{N^2}=0 is modified to the exact quantum relation (S^N-\Lambda^{3N})^N=0.Comment: 5 pages. Comments and references adde

Chiral rings, anomalies and loop equations in N=1* gauge theories

We examine the equivalence between the Konishi anomaly equations and the matrix model loop equations in N=1* gauge theories, the mass deformation of N=4 supersymmetric Yang-Mills. We perform the superfunctional integral of two adjoint chiral superfields to obtain an effective N=1 theory of the third adjoint chiral superfield. By choosing an appropriate holomorphic variation, the Konishi anomaly equations correctly reproduce the loop equations in the corresponding three-matrix model. We write down the field theory loop equations explicitly by using a noncommutative product of resolvents peculiar to N=1* theories. The field theory resolvents are identified with those in the matrix model in the same manner as for the generic N=1 gauge theories. We cover all the classical gauge groups. In SO/Sp cases, both the one-loop holomorphic potential and the Konishi anomaly term involve twisting of index loops to change a one-loop oriented diagram to an unoriented diagram. The field theory loop equations for these cases show certain inhomogeneous terms suggesting the matrix model loop equations for the RP2 resolvent.Comment: 23 pages, 3 figures, latex2e, v4: minor changes in introduction and conclusions, 4 references are added, version to appear in JHE

A note on instanton counting for N=2 gauge theories with classical gauge groups

We study the prepotential of N=2 gauge theories using the instanton counting techniques introduced by Nekrasov. For the SO theories without matter we find a closed expression for the full prepotential and its string theory gravitational corrections. For the more subtle case of Sp theories without matter we discuss general features and compute the prepotential up to instanton number three. We also briefly discuss SU theories with matter in the symmetric and antisymmetric representations. We check all our results against the predictions of the corresponding Seiberg-Witten geometries.Comment: 24 pages, LaTeX. v2: refs added. v3: typos correcte

Following the Nonthermal Phase Transition in Niobium Dioxide by Time-Resolved Harmonic Spectroscopy

Photoinduced phase transitions in correlated materials promise diverse applications from ultrafast switches to optoelectronics. Resolving those transitions and possible metastable phases temporally are key enablers for these applications, but challenge existing experimental approaches. Extreme nonlinear optics can help probe phase changes, as higher-order nonlinearities have higher sensitivity and temporal resolution to band structure and lattice deformations. Here the ultrafast transition from the semiconducting to the metallic phases in polycrystalline thin-film NbO2 is investigated by time-resolved harmonic spectroscopy. The emission strength of all harmonic orders shows a steplike suppression when the excitation fluence exceeds a threshold (∼11-12 mJ/cm2), below the fluence required for the thermal transition - a signature of the nonthermal emergence of a metallic phase within 100 ± 20 fs. This observation is backed by full ab initio simulations as well as a 1D chain model of high-harmonic generation from both phases. Our results demonstrate femtosecond harmonic probing of phase transitions and nonthermal dynamics in solids.</p

Glueball operators and the microscopic approach to N=1 gauge theories

We explain how to generalize Nekrasov's microscopic approach to N=2 gauge theories to the N=1 case, focusing on the typical example of the U(N) theory with one adjoint chiral multiplet X and an arbitrary polynomial tree-level superpotential Tr W(X). We provide a detailed analysis of the generalized glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa matrix model and of the generalized Konishi anomaly equations. We compute in particular the non-trivial quantum corrections to the Virasoro operators and algebra that generate these equations. We have performed explicit calculations up to two instantons, that involve the next-to-leading order corrections in Nekrasov's Omega-background.Comment: 38 pages, 1 figure and 1 appendix included; v2: typos and the list of references corrected, version to appear in JHE

Matrix Models, Monopoles and Modified Moduli

Motivated by the Dijkgraaf-Vafa correspondence, we consider the matrix model duals of N=1 supersymmetric SU(Nc) gauge theories with Nf flavors. We demonstrate via the matrix model solutions a relation between vacua of theories with different numbers of colors and flavors. This relation is due to an N=2 nonrenormalization theorem which is inherited by these N=1 theories. Specializing to the case Nf=Nc, the simplest theory containing baryons, we demonstrate that the explicit matrix model predictions for the locations on the Coulomb branch at which monopoles condense are consistent with the quantum modified constraints on the moduli in the theory. The matrix model solutions include the case that baryons obtain vacuum expectation values. In specific cases we check explicitly that these results are also consistent with the factorization of corresponding Seiberg-Witten curves. Certain results are easily understood in terms of M5-brane constructions of these gauge theories.Comment: 27 pages, LaTeX, 2 figure

Improved matrix-model calculation of the N=2 prepotential

We present a matrix-model expression for the sum of instanton contributions to the prepotential of an N=2 supersymmetric U(N) gauge theory, with matter in various representations. This expression is derived by combining the renormalization-group approach to the gauge theory prepotential with matrix-model methods. This result can be evaluated order-by-order in matrix-model perturbation theory to obtain the instanton corrections to the prepotential. We also show, using this expression, that the one-instanton prepotential assumes a universal form.Comment: 20 pages, LaTeX, 2 figure

Orbital Parameter Determination for Wide Stellar Binary Systems in the Age of Gaia

The orbits of binary stars and planets, particularly eccentricities and inclinations, encode the angular momentum within these systems. Within stellar multiple systems, the magnitude and (mis)alignment of angular momentum vectors among stars, disks, and planets probes the complex dynamical processes guiding their formation and evolution. The accuracy of the Gaia catalog can be exploited to enable comparison of binary orbits with known planet or disk inclinations without costly long-term astrometric campaigns. We show that Gaia astrometry can place meaningful limits on orbital elements in cases with reliable astrometry, and discuss metrics for assessing the reliability of Gaia DR2 solutions for orbit fitting. We demonstrate our method by determining orbital elements for three systems (DS Tuc AB, GK/GI Tau, and Kepler-25/KOI-1803) using Gaia astrometry alone. We show that DS Tuc AB's orbit is nearly aligned with the orbit of DS Tuc Ab, GK/GI Tau's orbit might be misaligned with their respective protoplanetary disks, and the Kepler-25/KOI-1803 orbit is not aligned with either component's transiting planetary system. We also demonstrate cases where Gaia astrometry alone fails to provide useful constraints on orbital elements. To enable broader application of this technique, we introduce the python tool lofti_gaiaDR2 to allow users to easily determine orbital element posteriors

TESTING the BINARY TRIGGER HYPOTHESIS in FUors

We present observations of three FU Orionis objects (hereafter, FUors) with nonredundant aperture-mask interferometry at 1.59 μm and 2.12 μm that probe for binary companions on the scale of the protoplanetary disk that feeds their accretion outbursts. We do not identify any companions to V1515 Cyg or HBC 722, but we do resolve a close binary companion to V1057 Cyg that is at the diffraction limit ( mas or 30 5 au) and currently much fainter than the outbursting star ( mag). Given the flux excess of the outbursting star, we estimate that the mass of the companion () is similar to or slightly below that of the FUor itself, and therefore it resembles a typical T Tauri binary system. Our observations only achieve contrast limits of mag, and hence we are only sensitive to companions that were near or above the pre-outburst luminosity of the FUors. It remains plausible that FUor outbursts could be tied to the presence of a close binary companion. However, we argue from the system geometry and mass reservoir considerations that these outbursts are not directly tied to the orbital period (i.e., occurring at periastron passage), but instead must only occur infrequently

Orbital architectures of planet-hosting binaries - II. Low mutual inclinations between planetary and stellar orbits

Planet formation is often considered in the context of one circumstellar disc around one star. Yet, stellar binary systems are ubiquitous, and thus a substantial fraction of all potential planets must form and evolve in more complex, dynamical environments. We present the results of a 5 yr astrometric monitoring campaign studying 45 binary star systems that host Kepler planet candidates. The planet-forming environments in these systems would have literally been shaped by the binary orbits that persist to the present day. Crucially, the mutual inclinations of star-planet orbits can only be addressed by a statistical sample. We describe in detail our sample selection and Keck/NIRC2 laser guide star adaptive optics observations collected from 2012 to 2017. We measure orbital arcs, with a typical accuracy of ∼0.1 mas yr-1, that test whether the binary orbits tend to be aligned with the edge-on transiting planet orbits. We rule out randomly distributed binary orbits at 4.7σ, and we show that low mutual inclinations are required to explain the observed orbital arcs. If the stellar orbits have a field binary-like eccentricity distribution, then the best match to our observed orbital arcs is a distribution of mutual inclinations ranging from 0° to 30°. We discuss the implications of such widespread planet-binary alignment in the theoretical context of planet formation and circumstellar disc evolution