Two-index Antisymmetric Representation Research Articles

Tetraquarks with exotic flavor quantum numbers at largeNcin QCD(AS)

It is shown that the large $N_c$ limit of QCD with quarks in the two-index antisymmetric color representation [QCD(AS)] has narrow tetraquark states with exotic flavor quantum numbers. They decay into mesons with a width that is parametrically $O(1/N_c^2)$. Tetraquarks with non-exotic quantum numbers mix at leading order with mesons of the same overall quantum numbers. QCD(AS) at $N_c=3$ corresponds to ordinary QCD; its large $N_c$ limit represents an alternative starting point for a $1/N_c$ expansion to the standard one with quarks in the fundamental color representation.

A note on Seiberg duality and chiral symmetry breaking

Following arXiv:1310.2027 and arXiv:0801.0762, we consider a non-supersymmetric Seiberg duality between electric and magnetic “orientifold field theories”. These theories live on brane configurations of type 0′ string theory. In the electric theory side the scalars acquire a mass and decouple, resulting in an SU(Nc) gauge theory coupled to Nf massless quarks and an additional massless fermion that transforms in the two-index antisymmetric representation. In the magnetic theory side there exists a fundamental meson field that develops a Coleman–Weinberg potential. At the one-loop approximation the potential admits a minimum with chiral symmetry breaking of the form SU(Nf)L×SU(Nf)R→SU(Nf)V and an additional breaking of an axial U(1) symmetry. The resulting theory admits a spectrum whose massless degrees of freedom are Nf2 Nambu–Goldstone bosons.

Near the sill of the conformal window: Gauge theories with fermions in two-index representations

We apply Schr\"odinger functional methods to two gauge theories with fermions in two-index representations: the SU(3) theory with ${N}_{f}=2$ adjoint fermions, and the SU(4) theory with ${N}_{f}=6$ fermions in the two-index antisymmetric representation. Each theory is believed to lie near the bottom of the conformal window for its respective representation. In the SU(3) theory we find a small beta function in strong coupling but we cannot confirm or rule out an infrared fixed point. In the SU(4) theory we find a hint of walking---a beta function that approaches the axis and then turns away from it. In both theories the mass anomalous dimension remains small even at the strongest couplings, much like the theories with fermions in the two-index symmetric representation investigated earlier.

Composite inflation from super Yang-Mills theory, orientifold, and one-flavor QCD

Recent investigations have shown that inflation can be driven by four-dimensional strongly interacting theories nonminimally coupled to gravity. We explore this paradigm further by considering composite inflation driven by orientifold field theories. The advantage of using these theories resides in the fact that at large number of colors they feature certain super Yang-Mills properties. In particular, we can use for inflation the bosonic part of the Veneziano-Yankielowicz effective theory. Furthermore, we include the $1/N$ as well as fermion mass corrections at the effective Lagrangian level allowing us to explore the effects of these corrections on the inflationary slow-roll parameters. Additionally, the orientifold field theory with fermionic matter transforming according to the two-index antisymmetric representation for three colors is QCD. Therefore, this model can be interpreted as a new nonminimally coupled QCD theory of inflation. The scale of composite inflation, for all the models presented here, is of the order of ${10}^{16}\text{ }\text{ }\mathrm{GeV}$. Unitarity studies of the inflaton scattering suggest that the cutoff of the model is at the Planck scale.

Baryon magnetic moments in alternate1/Ncexpansions

Recent work shows not only the necessity of a $1/{N}_{c}$ expansion to explain the observed mass spectrum of the lightest baryons, but also that at least two distinct large ${N}_{c}$ expansions, in which quarks transform under either the color-fundamental or the two-index antisymmetric representation of $\mathrm{SU}({N}_{c})$, work comparably well. Here we show that the baryon magnetic moments do not support this ambivalence; they strongly prefer the color-fundamental $1/{N}_{c}$ expansion, providing experimental evidence that nature decisively distinguishes among $1/{N}_{c}$ expansions for this observable.

Color superconductivity at largeN: A new hope

At zero density, the `t Hooft large N_c limit often provides some very useful qualitative insights into the non-perturbative physics of QCD. However, it is known that at high densities the `t Hooft large N_c world looks very different from the N_c=3 world, which is believed to be in a color superconducting phase at high densities. At large N_c, on the other hand, the DGR instability causes a chiral-density wave phase to dominate over the color superconducting phase. There is an alternative large N_c limit, with the quarks transforming in the two-index antisymmetric representation of the gauge group, which at N_c=3 reduces to QCD but looks quite different at large N_c. We show that in this alternative large N_c limit, the DGR instability does not occur, so that it may be plausible that the ground state of high-density quark matter is a color superconductor even when N_c is large. This revives the hope that a large N_c approximation might be useful for getting some insights into the high-density phenomenology of QCD.

Baryons inQCDASat largeNc: A roundabout approach

QCD_{AS}, a variant of large N_c QCD in which quarks transform under the color two-index antisymmetric representation, reduces to standard QCD at N_c = 3 and provides an alternative to the usual large N_c extrapolation that uses fundamental representation quarks. Previous strong plausibility arguments assert that the QCD_{AS} baryon mass scales as N_c^2; however, the complicated combinatoric problem associated with quarks carrying two color indices impeded a complete demonstration. We develop a diagrammatic technique to solve this problem. The key ingredient is the introduction of an effective multi-gluon vertex: a "traffic circle" or "roundabout" diagram. We show that arbitrarily complicated diagrams can be reduced to simple ones with the same leading N_c scaling using this device, and that the leading contribution to baryon mass does, in fact, scale as N_c^2.

All you need isN: Baryon spectroscopy in two largeNlimits

The generalization of QCD to many colors is not unique; each distinct choice corresponds to a distinct $1/{N}_{c}$ expansion. The familiar 't Hooft ${N}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit places quarks in the fundamental representation of $\mathrm{SU}({N}_{c})$, while an alternative approach places quarks in its two-index antisymmetric representation. At ${N}_{c}=3$ these two $1/{N}_{c}$ expansions coincide. We compare their predictions for certain observables in baryon spectroscopy, particularly mass combinations organized according to SU(3) flavor breaking. Each large ${N}_{c}$ limit generates an emergent spin-flavor symmetry that leads to the vanishing of particular linear combinations of baryon masses at specific orders in the expansions. Experimental evidence shows that these relations hold at the expected orders regardless of which large ${N}_{c}$ limit one uses, suggesting the validity of either limit in the study of baryons. We also consider a hybrid large ${N}_{c}$ limit in which one flavor is taken to transform in the two-index antisymmetric representation and the rest of the flavors are in the fundamental representation. While this hybrid large ${N}_{c}$ limit is theoretically attractive, we show that for a wide class of observables it faces some phenomenological difficulties.

Degeneracy between the Regge slope of mesons and baryons from supersymmetry

We consider the degeneracy between the Regge slope of mesons and baryons in QCD. We argue that within the "orientifold large-N approximation" asymptotically massive mesons and baryons become supersymmetric partners and hence degenerate. To this end, we generalize QCD by a SU(N) theory with a quark in the two-index antisymmetric representation. We show that in this framework the meson is represented by an oriented bosonic QCD-string and the baryon is represented by an un-oriented fermionic QCD-string. At large-N, due to an equivalence with super Yang-Mills, the tensions of the bosonic and the fermionic strings coincide. Our description of mesons and baryons as oriented and un-oriented bosonic and fermionic QCD-strings is in full agreement with the spectra of open strings in the dual type 0' string theory.

The Skyrmion strikes back: baryons and a new largeNclimit

In the large $N_c$ limit of QCD, baryons can be modeled as solitons, for instance, as Skyrmions. This modeling has been justified by Witten's demonstration that all properties of baryons and mesons scale with $N_c^{-1/2}$ in the same way as the analogous meson-based soliton model scales with a generic meson-meson coupling constant $g$. An alternative large $N_c$ limit (the orientifold large $N_c$ limit) has recently been proposed in which quarks transform in the two-index antisymmetric representation of $SU(N_c)$. By carrying out the analog of Witten's analysis for the new orientifold large $N_c$ limit, we show that baryons and solitons can also be identified in the orientifold large $N_c$ limit. However, in the orientifold large $N_c$ limit, the interaction amplitudes and matrix elements scale with $N_c^{-1}$ in the same way as soliton models scale with the generic meson coupling constant $g$ rather than as $N_c^{-1/2}$ as in the traditional large $N_c$ limit.

Effective Lagrangians for orientifold theories

We construct effective Lagrangians of the Veneziano-Yankielowicz (VY) type for two non-supersymmetric theories which are orientifold daughters of supersymmetric gluodynamics (containing one Dirac fermion in the two-index antisymmetric or symmetric representation of the gauge group). Since the parent and daughter theories are planar equivalent, at N\to\infty the effective Lagrangians in the orientifold theories basically coincide with the bosonic part of the VY Lagrangian. We depart from the supersymmetric limit in two ways. First, we consider finite (albeit large) values of N. Then 1/N effects break supersymmetry. We suggest seemingly the simplest modification of the VY Lagrangian which incorporates these 1/N effects, leading to a non-vanishing vacuum energy density. We analyze the spectrum of the finite-N non-supersymmetric daughters. For N=3 the two-index antisymmetric representation (one flavor) is equivalent to one-flavor QCD. We show that in this case the scalar quark-antiquark state is heavier than the corresponding pseudoscalar state, `` eta' ''. Second, we add a small fermion mass term. The fermion mass term breaks supersymmetry explicitly. The vacuum degeneracy is lifted. The parity doublets split. We evaluate the splitting. Finally, we include the theta-angle and study its implications.

Supersymmetry relics in one-flavor QCD from a new 1/N expansion.

We suggest a new large-N(c) limit for multiflavor QCD. Since fundamental and two-index antisymmetric representations are equivalent in SU(3), we have the option to define SU(N(c)) QCD keeping quarks in the latter. We can then define a new 1/N(c) expansion (at a fixed number of flavors N(f)) that shares appealing properties with the topological (fixed N(f)/N(c)) expansion while being more suitable for theoretical analysis. In particular, for N(f)=1, our large-N(c) limit gives a theory that we recently proved to be equivalent, in the bosonic sector, to N=1 supersymmetric gluodynamics. Using known properties of the latter, we derive several qualitative and semiquantitative predictions for N(f)=1 massless QCD that can be easily tested in lattice simulations. Finally, we comment on possible applications for pure SU(3) Yang-Mills theory and real QCD.