Philip C. Argyres

New Phenomena in SU(3) Supersymmetric Gauge Theory

We show that four-dimensional N = 2 supersymmetric SU(N) gauge theory for N > 2 necessarily contains vacua with mutually non-local massless dyons, using only analyticity of the effective action and the weak coupling limit of the moduli space of vacua. A specific example is the ℤ3 point in the exact solution for SU(3), and we study its effective Lagrangian. We propose that the low-energy theory at this point is an N = 2 superconformal U(1) gauge theory containing both electrically and magnetically charged massless hypermultiplets.

The vacuum structure and spectrum of N=2 supersymmetric SU(n) gauge theory

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional {ital N}=2 supersymmetric SU({ital n}) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus {ital n}{minus}1 hyperelliptic Riemann surfaces.

The Coulomb phase of N=2 supersymmetric QCD

We present an explicit nonperturbative solution of N=2 supersymmetric SU({ital N}) gauge theory with {ital N}{sub {ital f}}{le}2{ital N} flavors generalizing results of Seiberg and Witten for {ital N}=2.

BLACK HOLES AND SUB-MILLIMETER DIMENSIONS

Recently, a new framework for solving the hierarchy problem was proposed which does not rely on low energy supersymmetry or technicolor. The fundamental Planck mass is at a TeV and the observed weakness of gravity at long distances is due the existence of new sub-millimeter spatial dimensions. In this letter, we study how the properties of black holes are altered in these theories. Small black holes—with Schwarzschild radii smaller than the size of the new spatial dimensions—are quite different. They are bigger, colder, and longer-lived than a usual (3+1)-dimensional black hole of the same mass. Furthermore, they primarily decay into harmless bulk graviton modes rather than standard-model degrees of freedom. We discuss the interplay of our scenario with the holographic principle. Our results also have implications for the bounds on the spectrum of primordial black holes (PBHs) derived from the photo-dissociation of primordial nucleosynthesis products, distortion of the diffuse gamma-ray spectrum, overclosure of the universe, gravitational lensing, as well as the phenomenology of black hole production. For example, the bound on the spectral index of the primordial spectrum of density perturbations is relaxed from 1.25 to 1.45–1.60 depending on the epoch of the PBH formation. In these scenarios PBHs provide interesting dark matter candidates; for 6 extra dimensions MACHO candidates with mass ∼0.1M⊙ can arise. For 2 or 3 extra dimensions PBHs with mass ∼104M⊙ can occur and may act as both dark matter and seeds for early galaxy and QSO formation.

String webs from field theory

The spectrum of stable electrically and magnetically charged supersymmetric particles can change discontinuously as one changes the vacuum on the Coulomb branch of gauge theories with extended supersymmetry in four dimensions. We show that this decay process can be understood and is well described by semiclassical field configurations purely in terms of the low energy effective action on the Coulomb branch even when it occurs at strong coupling. The resulting picture of the stable supersymmetric spectrum is a generalization of the ``string web picture of these states found in string constructions for certain theories.

Mass deformations of four-dimensional, rank 1, N=2 superconformal field theories

Turning on N=2 supersymmetry preserving relevant operators in a 4-dimensional N=2 superconformal field theory (SCFT) corresponds to a complex deformation compatible with the rigid special Kahler (RSK) geometry encoded in the low energy effective action. Field theoretic consistency arguments indicate that there should be many distinct such relevant deformations of each SCFT fixed point. Some new RSK-compatible complex deformations are constructed of isolated rank 1 SCFTs. We also make predictions for the dimensions of Higgs branches for some rank 1 SCFTs.

On inherited duality in N=1 d = 4 supersymmetric gauge theories

Four-dimensional = 1 supersymmetric gauge theories with two adjoints and a quartic superpotential are believed, from AdS/CFT duality, to have SL(2,) invariance. In this note we review an old, unpublished argument for this property, based solely on field theory. The technique involves a complexified flavor rotation which deforms an = 2 supersymmetric gauge theory with matter to an = 1 theory, leaving all holomorphic invariants unchanged. We apply this to the = 1 gauge theory with two massless adjoints and show that it has the same auxiliary torus as that of = 4 gauge theory, from which SL(2,) invariance follows. In the appendix, we check that our arguments are consistent with earlier work on the SU(2) case. Our technique is general and applies to many other = 1 theories.

Comparing instanton contributions with exact results in N = 2 supersymmetric scale invariant theories

We discuss the general issues and ambiguities involved in matching the exact results for the low energy effective action of scale invariant = 2 supersymmetric QCD to those obtained by instanton methods. We resolve the reported disagreements and verify agreement between an infinite series of coefficients in the low energy effective actions calculated in the two approaches. In particular, we show that the exact low-energy effective couplings for SU(N) for all N with 2N fundamental hypermultiplets agree at a special vacuum on the Coulomb branch where a large unbroken discrete global symmetry makes the matching of parameters relatively straightforward.

Fractional Superstrings with Space-Time Critical Dimensions Four and Six

We propose possible new string theories based on local world-sheet symmetries corresponding to extensions of the Virasoro algebra by fractional spin currents. They have critical central charges c = 6(K + 8)/(K + 2) and Minkowski space-time dimensions D = 2+16/K for K ≥ 2 an integer. We present evidence for their existence by constructing modular invariant partition functions and the massless particle spectra. The dimension 4 and 6 strings have space-time supersymmetry. String theories[1] are primarily characterized by the local symmetries of a twodimensional field theory on the string world-sheet. The local symmetries of the bosonic string are reparameterization and Weyl invariance which lead to a critical string propagating in 26 flat space-time dimensions. The superstring enlarges the world-sheet gauge invariance to include a local N = 1 supersymmetry, and reduces the critical space-time dimension to 10. It is natural to try to construct string theories with smaller critical space-time dimensions by changing the worldsheet symmetry. Unfortunately, enlarging to a local N = 2 supersymmetry produces a critical string in just two-dimensional Minkowski space. It is well known, however, that fractionalspin fields can exist in two-dimensional field theory. One can imagine new local symmetries on the world-sheet which involve fractional-spin currents and which lead to string propagation in space-times with dimensions less than 10. In this letter we will present evidence for the existence of such new string theories, and in particular will show that strings with spin 4/3 and 6/5 currents on the world-sheet can have interesting phenomenologies in 6 and 4 space-time dimensions, respectively. The algebra of constraints resulting from gauge-fixing the two-dimensional local symmetry must contain the Virasoro algebra. In this letter we consider strings with

New Jacobi-like identities for ZK parafermion characters

We state and prove various new identities involving theZK parafermion characters (or level-K string functions)cnl for the casesK=4,K=8, andK=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi ϑ-function identity (which is theK=2 special case), identities in another class relate the levelK>2 characters to the Dedekind η-function, and identities in a third class relate theK>2 characters to the Jacobi ϑ-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states.