SQCD Research Articles

Analytic coupling structure of large Nf (super) QED and QCD

We study the analytic properties of the 't Hooft coupling expansion of the beta-function at the leading nontrivial large-$N_f$ order for QED, QCD, Super QED and Super QCD. For each theory, the 't Hooft coupling expansion is convergent. We discover that an analysis of the expansion coefficients to roughly 30 orders is required to establish the radius of convergence accurately, and to characterize the (logarithmic) nature of the first singularity. We study summations of the beta-function expansion at order $1/N_f$, and identify the physical origin of the singularities in terms of iterated bubble diagrams. We find a common analytic structure across these theories, with important technical differences between supersymmetric and non-supersymmetric theories. We also discuss the expected structure at higher orders in the $1/N_f$ expansion, which will be in the future accessible with the methods presented in this work, meaning without the need for resumming the perturbative series. Understanding the structure of the large-$N_f$ expansion is an essential step towards determining the ultraviolet fate of asymptotically non-free gauge theories.

Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)

We study the domain walls in hot 4-D SU(N) super Yang-Mills theory and QCD(adj), with nf Weyl flavors. We find that the k-wall worldvolume theory is 2-D QCD with gauge group SU(N − k) × SU(k) × U(1) and Dirac fermions charged under U(1) and transforming in the bi-fundamental representation of the nonabelian factors. We show that the DW theory has a 1-form ℤN(1) center symmetry and a 0-form {mathbb{Z}}_{2N{n}_f}^{dchi } discrete chiral symmetry, with a mixed ’t Hooft anomaly consistent with bulk/wall anomaly inflow. We argue that ℤN(1) is broken on the wall, and hence, Wilson loops obey the perimeter law. The breaking of the worldvolume center symmetry implies that bulk p-strings can end on the wall, a phenomenon first discovered using string-theoretic constructions. We invoke 2-D bosonization and gauged Wess-Zumino-Witten models to suggest that {mathbb{Z}}_{2N{n}_f}^{dchi } is also broken f in the IR, which implies that the 0-form/1-form mixed ’t Hooft anomaly in the gapped k-wall theory is saturated by a topological quantum field theory. We also find interesting parallels between the physics of high-temperature domain walls studied here and domain walls between chiral symmetry breaking vacua in the zero temperature phase of the theory (studied earlier in the semiclassically calculable small spatial circle regime), arising from the similar mode of saturation of the relevant ’t Hooft anomalies.

4D gauge theories with conformal matter

One of the hallmarks of 6D superconformal field theories (SCFTs) is that on a partial tensor branch, all known theories resemble quiver gauge theories with links comprised of 6D conformal matter, a generalization of weakly coupled hypermultiplets. In this paper we construct 4D quiverlike gauge theories in which the links are obtained from compactifications of 6D conformal matter on Riemann surfaces with flavor symmetry fluxes. This includes generalizations of super QCD with exceptional gauge groups and quarks replaced by 4D conformal matter. Just as in super QCD, we find evidence for a conformal window as well as confining gauge group factors depending on the total amount of matter. We also present F-theory realizations of these field theories via elliptically fibered Calabi-Yau fourfolds. Gauge groups (and flavor symmetries) come from 7-branes wrapped on surfaces, conformal matter localizes at the intersection of pairs of 7-branes, and Yukawas between 4D conformal matter localize at points coming from triple intersections of 7-branes. Quantum corrections can also modify the classical moduli space of the F-theory model, matching expectations from effective field theory.

Safe SUSY

We investigate the short distance fate of distinct classes of not asymptotically free supersymmetric gauge theories. Examples include super QCD with two adjoint fields and generalised superpotentials, gauge theories without superpotentials and with two types of matter representation and semi-simple gauge theories such as quivers. We show that for the aforementioned theories asymptotic safety is nonperturbatively compatible with all known constraints.

Two dimensional super QCD on a lattice

We construct a lattice theory with one exact supersymmetry which consists of fields transforming in both the adjoint and fundamental representations of a U(Nc) gauge group. In addition to gluons and gluinos, the theory contains Nf flavors of fermion in the fundamental representation along with their scalar partners and is invariant under a global U(Nf) flavor symmetry. The lattice action contains an additional Fayet-Iliopoulos term which can be used to generate a scalar potential. We perform numerical simulations that corroborate the theoretical expectation that supersymmetry is spontaneously broken for Nf<Nc.

$R$-symmetric Super-QCD at the NLO

$R$-symmetric Super-QCD at the NLO

Spontaneous supersymmetry breaking in two dimensional lattice super QCD

We report on a non-perturbative study of two dimensional $$ \mathcal{N}=\left(2,2\right) $$ super QCD. Our lattice formulation retains a single exact supersymmetry at non-zero lattice spacing, and contains N f fermions in the fundamental representation of a U(N c ) gauge group. The lattice action we employ contains an additional Fayet-Iliopoulos term which is also invariant under the exact lattice supersymmetry. This work constitutes the first numerical study of this theory which serves as a toy model for understanding some of the issues that are expected to arise in four dimensional super QCD. We present evidence that the exact supersymmetry breaks spontaneously when N f < N c in agreement with theoretical expectations.

The complete one-loop spin chain of $ \mathcal{N} $ = 1 SQCD

We evaluate the complete planar one-loop dilation operator of N=1 Super QCD, at the large N Bank-Zaks fixed point near the upper edge of the superconformal window. The spin-chain Hamiltonian turns out to be entirely fixed by the constraints of superconformal symmetry, as in N=4 Super Yang-Mills and in N=2 SuperConformal QCD.

Naturalness from runaways in direct mediation

Postulating that the NMSSM singlet is a meson of a microscopic confining theory opens up new model-building possibilities. Based on this, we construct calculable models of direct mediation that solve the mu/Bmu problem and simultaneously lead to realistic phenomenology. The singlet that couples to the Higgs fields develops a runaway produced by soft interactions, then stabilized by a small superpotential perturbation. The mechanism is first realized in an O'Raifeartaigh model of direct gauge mediation with metastable supersymmetry breaking. Focusing then on the microscopic theory, we argue that super QCD with massless and massive flavors in the free magnetic phase gives rise to this dynamics in the infrared. A deformation of the SQCD superpotential leads to large spontaneous R-symmetry breaking, gaugino masses naturally at the scale of the Higgs mass parameters, and absence of CP violating phases.

Nonsupersymmetric Seiberg duality, orientifold QCD, and noncritical strings

We propose an electric-magnetic duality and conjecture an exact conformal window for a class of nonsupersymmetric $U({N}_{c})$ gauge theories with fermions in the (anti)symmetric representation of the gauge group and ${N}_{f}$ additional scalar and fermion flavors. The duality exchanges ${N}_{c}\ensuremath{\rightarrow}{N}_{f}\ensuremath{-}{N}_{c}\ensuremath{\mp}4$ leaving ${N}_{f}$ invariant, and has common features with Seiberg duality in $\mathcal{N}=1$ super QCD (SQCD) with $SU$ or $SO/Sp$ gauge group. At large $N$ the duality holds due to planar equivalence with $\mathcal{N}=1$ SQCD. At finite $N$ we embed these gauge theories in a setup with D-branes and orientifolds in a nonsupersymmetric, but tachyon-free, noncritical type 0B string theory and argue in favor of the duality in terms of boundary and crosscap state monodromies as in analogous supersymmetric situations. One can verify explicitly that the resulting duals have matching global anomalies. Finally, we comment on the moduli space of these gauge theories and discuss other potential nonsupersymmetric examples that could exhibit similar dualities.

Three dimensionalN= 2 supersymmetry on the lattice

We show how 3-dimensional, N=2 supersymmetric theories, including super QCD with matter fields, can be put on the lattice with existing techniques, in a way which will recover supersymmetry in the small lattice spacing limit. Residual supersymmetry breaking effects are suppressed in the small lattice spacing limit by at least one power of the lattice spacing a.

N = 1 super quantum chromo dynamics and fractional branes

In this talk we show how to get the one-loop beta function and the chiral anomaly ofN = 1 super QCD from a stack of fractionalN D3-branes localized inside the world-volume of 2M fractionalD7-branes in the orbifoldC 3/(Z 2 ×Z 2). They are obtained by analyzing the classical supergravity background generated by such a brane configuration, in the spirit of the gauge/gravity correspondence.

Type IIB 2-form fields and gauge coupling constant of 4D ${\cal N}=2$ super QCD

We study the relation between the Type IIB (NSNS and RR) 2-form fields and the (complex) gauge coupling constant of the 4D N=2 SU(Nc) super Yang-Mills theory with Nf fundamental matters. We start from the analysis of the D2-brane world volume theory with heavy Nc quarks on the Nf D6 supergravity background. After a sequence of T- and S-dualities, we obtain the (generalized) 2-forms in the configuration with Nc D5-branes wrapping on the vanishing two-cycle under the influence of the background. These 2-forms shows the same behavior as the gauge coupling constant of the 4D N=2 super QCD. The background reduces to the Z_{Nf} orbifold in the twelve-dimensional space-time formally realized by introducing the two parameters as the additional space coordinates. The 10D gravity dual is suggested as the 2D flip in this twelve-dimensional space-time. In the case of Nf=2Nc, this gravity dual becomes AdS_5 \times S^5/Z_2 with D3-charge which depends on the constant generalized NSNS 2-form. This is the result expected from the M-theory QCD configuration. Based on the known exact result, we also discuss this configuration after including the nonperturbative effect.

BPS string solutions in non-Abelian Yang-Mills theories and confinement

Starting from the bosonic part of N=2 Super QCD with a 'Seiberg-Witten' N=2 breaking mass term, we obtain string BPS conditions for arbitrary semi-simple gauge groups. We show that the vacuum structure is compatible with a symmetry breaking scheme which allows the existence of Z_k-strings and which has Spin(10) -> SU(5) x Z_2 as a particular case. We obtain BPS Z_k-string solutions and show that they satisfy the same first order differential equations as the BPS string for the U(1) case. We also show that the string tension is constant, which may cause a confining potential between monopoles increasing linearly with their distance.

D0-Branes as Instantons in D = 4 Super Yang-Mills Theories

We discuss the role of D0-branes as instantons in the construction of SU(N) Super Yang-Mills and Super QCD theories in four space-time dimensions with D4-, D6- and NS-branes. [To appear in the proceedings of the conference "Quantum Aspects of Gauge Theories, Supersymmetry and Unification", held at Neuchatel University, Neuchatel, Switzerland, 18--23 September 1997.]

Branes and theta dependence

We use the fivebrane of M theory to study the θ dependence of four dimensional SU( N c ) super Yang-Mills and super QCD softly broken by a gaugino mass. We compute the energy of the vacuum in the supergravity approximation. The results obtained are in qualitative agreement with field theory. We also study the θ dependence of the QCD string tension via the fivebrane.

D0-branes, constrained instantons and D = 4 Super Yang-Mills theories

We consider in more detail the role of D0-branes as instantons in the construction of SU( N) Super Yang-Mills and Super QCD theories in four space-time dimensions with D4-, D6- and NS branes. In particular, we show how the D0-branes describe both the exact and constrained instantons and reproduce the correct pattern of lifting of zero-modes on the various branches of these models.

Toy model for breaking super gauge theories at the effective Lagrangian level

We propose a toy model to illustrate how the effective Lagrangian for super QCD might go over to the one for ordinary QCD by a mechanism whereby the gluinos and squarks in the fundamental theory decouple below a given supersymmetry breaking scale $m$. The implementation of this approach involves a suitable choice of possible supersymmetry breaking terms. An amusing feature of the model is the emergence of the ordinary QCD degrees of freedom which were hidden in the auxiliary fields of the supersymmetric effective Lagrangian.

Dynamical properties of the vacuum in non-abelian field theories with and without supersymmetry

In QCD with massless quarks, the effective potential for the color singlet operator ( F μν a ) 2 can be constructed by the use of the trace anomaly equation and tells us that magnetic gluon condensation, 〈0|( F μν a ) 2|0〉 > 0, occurs. When the method is applied to supersymmetric QCD, however, it gives us a puzzle; the gluons condense with negative energy density, and supersymmetry is broken in a pathological manner with the appearance of a negatively normed Nambu-Goldstone fermion. Spurred on by this observation, we examine in detail the properties of the vacuum for the super (and ordinary) O( N) non-linear σ model in two dimensions for which a similar puzzling situation occurs with regard to the lagrangian condensate. We find, in particular, that (i) the chiral condensate plays a crucial role in resolving the puzzle and that (ii) it is the nature of the response of the lagrangian condensate to the test charge, not the sign or the magnitude of the condensate itself, that determines the phase of the system. Implications of these results for (super) QCD, including an unconventional possibility of “electric” gluon condensation, are discussed.