A New Method for Finding Vacua in String Phenomenology

One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given string-phenomenological system in a huge class. In particular, this paper reviews and then extends hep-th/0606122 to include various non-perturbative effects. These include gaugino condensation and instantonic contributions to the superpotential.Comment: 27 pages, 5 .eps figures. V2: Minor corrections, reference adde

SQCD: A Geometric Apercu

We take new algebraic and geometric perspectives on the old subject of SQCD. We count chiral gauge invariant operators using generating functions, or Hilbert series, derived from the plethystic programme and the Molien-Weyl formula. Using the character expansion technique, we also see how the global symmetries are encoded in the generating functions. Equipped with these methods and techniques of algorithmic algebraic geometry, we obtain the character expansions for theories with arbitrary numbers of colours and flavours. Moreover, computational algebraic geometry allows us to systematically study the classical vacuum moduli space of SQCD and investigate such structures as its irreducible components, degree and syzygies. We find the vacuum manifolds of SQCD to be affine Calabi-Yau cones over weighted projective varieties.Comment: 49 pages, 1 figur

Yukawa Couplings in Heterotic Compactification

We present a practical, algebraic method for efficiently calculating the Yukawa couplings of a large class of heterotic compactifications on Calabi-Yau three-folds with non-standard embeddings. Our methodology covers all of, though is not restricted to, the recently classified positive monads over favourable complete intersection Calabi-Yau three-folds. Since the algorithm is based on manipulating polynomials it can be easily implemented on a computer. This makes the automated investigation of Yukawa couplings for large classes of smooth heterotic compactifications a viable possibility.Comment: 38 page

Stability Walls in Heterotic Theories

We study the sub-structure of the heterotic Kahler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some regions of the Kahler moduli space but break supersymmetry in others. In the context of the four-dimensional theory, we investigate what happens when the Kahler moduli are changed from the supersymmetric to the non-supersymmetric region. Our results provide a low-energy description of supersymmetry breaking by internal gauge fields as well as a physical picture for the mathematical notion of bundle stability. Specifically, we find that at the transition between the two regions an additional anomalous U(1) symmetry appears under which some of the states in the low-energy theory acquire charges. We compute the associated D-term contribution to the four-dimensional potential which contains a Kahler-moduli dependent Fayet-Iliopoulos term and contributions from the charged states. We show that this D-term correctly reproduces the expected physics. Several mathematical conclusions concerning vector bundle stability are drawn from our arguments. We also discuss possible physical applications of our results to heterotic model building and moduli stabilization.Comment: 37 pages, 4 figure

Trust in financial services: Retrospect and prospect

Fostering and maintaining high levels of trust in the financial services sector is seen as crucial because of the characteristics of many financial service and in order to promote consumer engagement in the sector. In this article, we report evidence from a body of work and other commentary to provide an insight into trends in consumer trust in the sector as a whole, in comparison with other organisations and how different types of financial services provider have performed relative to each other. We show that the financial services sector as a whole is trusted more than some comparator institutions, and that aggregate levels of trust in the sector have fluctuated a relatively small amount subsequent to the financial crisis. However, important differences between provider types are apparent and these differences have become more profound in the recent past. We provide suggestions as to how trust in the sector may be improved and provider an analysis of current initiatives to improve trust levels in the sector in general and in banking in particular

The Space Density of Intermediate-redshift, Extremely Compact, Massive Starburst Galaxies

© 2022. The Author(s). Published by the American Astronomical Society. This is an open access article distributed under the Creative Commons Attribution License, to view a copy of the license, see: https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/We present a measurement of the intrinsic space density of intermediate-redshift (z ∼ 0.5), massive (M * ∼ 1011 M ⊙), compact (R e ∼ 100 pc) starburst (ΣSFR ∼ 1000 M ⊙ yr−1 kpc−1) galaxies with tidal features indicative of them having undergone recent major mergers. A subset of them host kiloparsec-scale, > 1000 km s−1 outflows and have little indication of AGN activity, suggesting that extreme star formation can be a primary driver of large-scale feedback. The aim for this paper is to calculate their space density so we can place them in a better cosmological context. We do this by empirically modeling the stellar populations of massive, compact starburst galaxies. We determine the average timescale on which galaxies that have recently undergone an extreme nuclear starburst would be targeted and included in our spectroscopically selected sample. We find that massive, compact starburst galaxies targeted by our criteria would be selectable for ∼148−24+27 Myr and have an intrinsic space density nCS∼(1.1−0.3+0.5)×10−6Mpc−3 . This space density is broadly consistent with our z ∼ 0.5 compact starbursts being the most extremely compact and star-forming low-redshift analogs of the compact star-forming galaxies in the early universe, as well as them being the progenitors to a fraction of intermediate-redshift, post-starburst, and compact quiescent galaxies.Peer reviewe

The Ionization and Dynamics of the Makani Galactic Wind

© 2023 The Author(s). Published by the American Astronomical Society. This is an open access article distributed under the Creative Commons Attribution License, to view a copy of the license, see: https://creativecommons.org/licenses/by/4.0/The Makani galaxy hosts the poster child of a galactic wind on scales of the circumgalactic medium. It consists of a two-episode wind in which the slow, outer wind originated 400 Myr ago (Episode I; R I = 20 − 50 kpc) and the fast, inner wind is 7 Myr old (Episode II; R II = 0 − 20 kpc). While this wind contains ionized, neutral, and molecular gas, the physical state and mass of the most extended phase—the warm, ionized gas—are unknown. Here we present Keck optical spectra of the Makani outflow. These allow us to detect hydrogen lines out to r = 30–40 kpc and thus constrain the mass, momentum, and energy in the wind. Many collisionally excited lines are detected throughout the wind, and their line ratios are consistent with 200–400 km s−1 shocks that power the ionized gas, with v shock = σ wind. Combining shock models, density-sensitive line ratios, and mass and velocity measurements, we estimate that the ionized mass and outflow rate in the Episode II wind could be as high as those of the molecular gas: MIIHII∼MIIH2=(1−2)×109M⊙ and dM/dtIIHII∼dM/dtIIH2=170−250M⊙ yr−1. The outer wind has slowed, so that dM/dtIHII∼10M⊙ yr−1, but it contains more ionized gas, MIHII=5×109 M ⊙. The momentum and energy in the recent Episode II wind imply a momentum-driven flow (p “boost” ∼7) driven by the hot ejecta and radiation pressure from the Eddington-limited, compact starburst. Much of the energy and momentum in the older Episode I wind may reside in a hotter phase, or lie further into the circumgalactic medium.Peer reviewe

Physical Properties of Massive Compact Starburst Galaxies with Extreme Outflows

© 2021. The Author(s). Published by the American Astronomical Society. This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/by/4.0/We present results on the nature of extreme ejective feedback episodes and the physical conditions of a population of massive (M * ∼ 1011 M ⊙), compact starburst galaxies at z = 0.4–0.7. We use data from Keck/NIRSPEC, SDSS, Gemini/GMOS, MMT, and Magellan/MagE to measure rest-frame optical and near-IR spectra of 14 starburst galaxies with extremely high star formation rate surface densities (mean ΣSFR ∼ 2000 M ⊙ yr−1 kpc−2) and powerful galactic outflows (maximum speeds v 98 ∼ 1000–3000 km s−1). Our unique data set includes an ensemble of both emission ([O ii] λλ3726,3729, Hβ, [O iii] λλ4959,5007, Hα, [N ii] λλ6549,6585, and [S ii] λλ6716,6731) and absorption (Mg ii λλ2796,2803, and Fe ii λ2586) lines that allow us to investigate the kinematics of the cool gas phase (T ∼ 104 K) in the outflows. Employing a suite of line ratio diagnostic diagrams, we find that the central starbursts are characterized by high electron densities (median n e ∼ 530 cm−3), and high metallicity (solar or supersolar). We show that the outflows are most likely driven by stellar feedback emerging from the extreme central starburst, rather than by an AGN. We also present multiple intriguing observational signatures suggesting that these galaxies may have substantial Lyman continuum (LyC) photon leakage, including weak [S ii] nebular emission lines. Our results imply that these galaxies may be captured in a short-lived phase of extreme star formation and feedback where much of their gas is violently blown out by powerful outflows that open up channels for LyC photons to escape.Peer reviewedFinal Published versio