Matthew J. Strassler

Exactly marginal operators and duality in four dimensional N = 1 supersymmetric gauge theory

Abstract We show that manifolds of fixed points, which are generated by exactly marginal operators, are common in N = 1 supersymmetric gauge theory. We present a unified and simple prescription for identifying these operators, using tools similar to those employed in two-dimensional N = 2 supersymmetry. In particular we rely on the work of Shifman and Vainshtein relating the β-function of the gauge coupling to the anomalous dimensions of the matter fields. Finite N = 1 models, which have marginal operators at zero coupling, are easily identified using our approach. The method can also be employed to find manifolds of fixed points which do not include the free theory; these are seen in certain models with product gauge groups and in many non-renormalizable effective theories. For a number of our models, S-duality may have interesting implications. Using the fact that relevant perturbations often cause one manifold of fixed points to flow to another, we propose a specific mechanism through which the N = 1 duality discovered by Seiberg could be associated with the duality of finite N = 2 models.

Hard scattering and gauge / string duality

We consider high-energy fixed-angle scattering of glueballs in confining gauge theories that have supergravity duals. Although the effective description is in terms of the scattering of strings, we find that the amplitudes are hard (power law). This is a consequence of the warped geometry of the dual theory, which has the effect that in an inertial frame the string process is never in the soft regime. At small angle we find hard and Regge behaviors in different kinematic regions.

Aspects of N = 2 supersymmetric gauge theories in three dimensions

Abstract We consider general aspects of N = 2 gauge theories in three dimensions, including their multiplet structure, anomalies and non-renormalization theorems. For U (1) gauge theories, we discuss the quantum corrections to the moduli space, and their relation to “mirror symmetries” of 3d N = 4 theories. Mirror symmetry is given an interpretation in terms of vortices. For SU ( N c ) gauge groups with N f fundamental flavors, we show that, depending on the number of flavors, there are quantum moduli spaces of vacua with various phenomena near the origin.

Echoes of a hidden valley at hadron colliders

Abstract We consider examples of “hidden-valley” models, in which a new confining gauge group is added to the standard model. Such models often arise in string constructions, and elsewhere. The resulting (electrically-neutral) bound states can have low masses and long lifetimes, and could be observed at the LHC and Tevatron. Production multiplicities are often large. Final states with heavy flavor are common; lepton pairs, displaced vertices and/or missing energy are possible. Accounting for LEP constraints, we find LHC production cross-sections typically in the 1–100 fb range, though they can be larger. It is possible the Higgs boson could be discovered at the Tevatron through rare decays to the new particles.

The Pomeron and gauge/string duality

The traditional description of high-energy small-angle scattering in QCD has two components — a soft Pomeron Regge pole for the tensor glueball, and a hard BFKL Pomeron in leading order at weak coupling. On the basis of gauge/string duality, we present a coherent treatment of the Pomeron. In large-N QCD-like theories, we use curved-space string-theory to describe simultaneously both the BFKL regime and the classic Regge regime. The problem reduces to finding the spectrum of a single j-plane Schrodinger operator. For ultraviolet-conformal theories, the spectrum exhibits a set of Regge trajectories at positive t, and a leading j-plane cut for negative t, the cross-over point being model-dependent. For theories with logarithmically-running couplings, one instead finds a discrete spectrum of poles at all t, where the Regge trajectories at positive t continuously become a set of slowly-varying and closely-spaced poles at negative t. Our results agree with expectations for the BFKL Pomeron at negative t, and with the expected glueball spectrum at positive t, but provide a framework in which they are unified. Effects beyond the single Pomeron exchange are briefly discussed.

Jet Substructure at the Tevatron and LHC: New results, new tools, new benchmarks

In this paper, we review recent theoretical progress and the latest experimental results in jet substructure from the Tevatron and the LHC. We review the status of and outlook for calculation and simulation tools for studying jet substructure. Following up on the report of the Boost 2010 workshop, we present a new set of benchmark comparisons of substructure techniques, focusing on the set of variables and grooming methods that are collectively known as ‘top taggers’. To facilitate further exploration, we have attempted to collect, harmonize and publish software implementations of these techniques.

The Duality cascade

The duality cascade, and its dual description as string theory on the warped deformed conifold, brings together several sophisticated topics, some of which are not widely known. These lectures, which contain a number of previously unpublished results, and are intended for experts as well as students, seek to explain the physics of duality cascades. Seiberg duality is carefully introduced, with detailed attention to the physical implications of duality away from the far infrared. The conifold is briefly introduced and strings on the conifold (the Klebanov-Witten model) are discussed. Next, fractional branes are introduced. The duality cascade is then constructed in field theory and in its dual supergravity description. Among the newly published results: it is shown why supergravity sees the cascade as smooth; how the two holomorphic couplings (dilaton and integrated two-form in supergravity) are related to the three physical couplings in the gauge theory; that there are actually twice as many approximate fixed points in the cascade as might be naively expected. These notes are based on lectures given at TASI 2003 and at the 2003 PIMS Summer School on Strings, Gravity & Cosmology.

Discovering the Higgs through highly-displaced vertices

We suggest that the Higgs could be discovered at the Tevatron or the LHC (perhaps at the LHCb detector) through decays with one or more substantially displaced vertices from the decay of new neutral particles. This signal may occur with a small but measurable branching fraction in the recently-described “hidden valley” models, hep-ph/0604261; weakly-coupled models with multiple scalars, including those of hep-ph/0511250, can also provide such signals, potentially with a much larger branching fraction. This decay channel may extend the Higgs mass reach for the Tevatron. Unusual combinations of b jets, lepton pairs and/or missing energy may accompany this signal.

Phenomenology of hidden valleys at hadron colliders

We study the phenomenology of, and search techniques for, a class of ``Hidden Valleys. These models are characterized by low mass (well below a TeV) bound states resulting from a confining gauge interaction in a hidden sector; the states include a spin-one resonance that can decay to lepton pairs. Assuming that the hidden sector communicates to the Standard Model (SM) through TeV suppressed operators, taking into account the constraint from the Z pole physics at LEP, searches at Tevatron may be difficult in the particular class of Hidden Valleys we consider, so that we concentrate on the searches at the LHC. Hidden Valley events are characterized by high multiplicities of jets and leptons in the final state. Depending on the scale of confinement in the hidden sector, the events are typically more spherical, with lower thrust and higher incidences of isolated leptons, than those from the SM background processes. Most notably, high cluster invariant mass and very narrow, low mass resonances in lepton pairs are the key observables to identify the signal. We use these characteristics to develop a set of cuts to separate the Hidden Valley from SM, and show that with these cuts LHC has a significant reach in the parameter space. Our strategies are quite general and should apply well beyond the particular class of models studied here.

A comment on entropy and area

For an arbitrary quantum field in flat space with a planar boundary, an entropy of entanglement, associated with correlations across the boundary, is present when the field is in its vacuum state. The vacuum state of the same quantum field appears thermal in Rindler space, with an associated thermal entropy. We show that the density matrices describing the two situations are identical, and therefore that the two entropies are equal. We comment on the generality and significance of this result, and make use of it in analyzing the area and cutoff dependence of the entropy. The equivalence of the density matrices leads us to speculate that a planar boundary in Minkowski space has a classical entropy given by the Bekenstein--Hawking formula.