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Register a new userEffective long distance $qbar{q} $ potential in holographic RG flows
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We study the $qbar{q}$ potential in strongly coupled non-conformal field theories with a non-trivial renormalization group flow via holography. We focus on the properties of this potential at an inter-quark separation $L$ large compared to the characteristic scale of the field theory. These are determined by the leading order IR physics plus a series of corrections, sensitive to the properties of the RG-flow. To determine those corrections, we propose a general method applying holographic Wilsonian renormalization to a dual string. We apply this method to examine in detail two sets of examples, $3+1$-dimensional theories with an RG flow ending in an IR fixed point; and theories that are confining in the IR, in particular, the Witten QCD and Klebanov-Strassler models. In both cases, we find corrections with a universal dependence on the inter-quark separation. When there is an IR fixed point, that correction decays as a power $sim 1/L^4$. We explain that dependence in terms of a double-trace deformation in a one-dimensional defect theory. For a confining theory, the decay is exponential $sim e^{-ML}$, with $M$ a scale of the order of the glueball mass. We interpret this correction using an effective flux tube description as produced by a background internal mode excitation induced by sources localized at the endpoints of the flux tube. We discuss how these results could be confronted with lattice QCD data to test whether the description of confinement via the gauge/gravity is qualitatively correct.
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Recent discoveries by Belle and BESIII of charged exotic quarkonium-like resonances provide fresh impetus for study of heavy exotic hadrons. In the limit N_c --> infinity, M_Q --> infinity, the (Qbar Q qbar q) tetraquarks (TQ-s) are expected to be narrow and slightly below or above the (Qbar q) and (Q qbar) two-meson threshold. The isoscalar TQ-s manifest themselves by decay to (Qbar Q) pi pi, and the ~30 MeV heavier charged isotriplet TQ-s by decays into (Qbar Q) pi. The new data strongly suggest that the real world with N_c=3, Q=c,b and q,q = u,d is qualitatively described by the above limit. We discuss the relevant theoretical estimates and suggest new signatures for TQ-s in light of the recent discoveries. We also consider baryon-like states (Q Q qbar qbar), which if found will be direct evidence not just for near-threshold binding of two heavy mesons, but for genuine tetraquarks with novel color networks. We stress the importance of experimental search for doubly-heavy baryons in this context.
We construct numerically finite density domain-wall solutions which interpolate between two $AdS_4$ fixed points and exhibit an intermediate regime of hyperscaling violation, with or without Lifshitz scaling. Such RG flows can be realized in gravitational models containing a dilatonic scalar and a massive vector field with appropriate choices of the scalar potential and couplings. The infrared $AdS_4$ fixed point describes a new ground state for strongly coupled quantum systems realizing such scalings, thus avoiding the well-known extensive zero temperature entropy associated with $AdS_2 times mathbb{R}^2$. We also examine the zero temperature behavior of the optical conductivity in these backgrounds and identify two scaling regimes before the UV CFT scaling is reached. The scaling of the conductivity is controlled by the emergent IR conformal symmetry at very low frequencies, and by the intermediate scaling regime at higher frequencies.
Boundary, defect, and interface RG flows, as exemplified by the famous Kondo model, play a significant role in the theory of quantum fields. We study in detail the holographic dual of a non-conformal supersymmetric impurity in the D1/D5 CFT. Its RG flow bears similarities to the Kondo model, although unlike the Kondo model the CFT is strongly coupled in the holographic regime. The interface we study preserves $d = 1$ $mathcal{N} = 4$ supersymmetry and flows to conformal fixed points in both the UV and IR. The interfaces UV fixed point is described by $d = 1$ fermionic degrees of freedom, coupled to a gauge connection on the CFT target space that is induced by the ADHM construction. We briefly discuss its field-theoretic properties before shifting our focus to its holographic dual. We analyze the supergravity dual of this interface RG flow, first in the probe limit and then including gravitational backreaction. In the probe limit, the flow is realized by the puffing up of probe branes on an internal $mathsf{S}^3$ via the Myers effect. We further identify the backreacted supergravity configurations dual to the interface fixed points. These supergravity solutions provide a geometric realization of critical screening of the defect degrees of freedom. This critical screening arises in a way similar to the original Kondo model. We compute the $g$-factor both in the probe brane approximation and using backreacted supergravity solutions, and show that it decreases from the UV to the IR as required by the $g$-theorem.
Axionic holographic RG flow solutions are studied in the context of general Einstein-Axion-Dilaton theories. A non-trivial axion profile is dual to the (non-perturbative) running of the $theta$-term for the corresponding instanton density operator. It is shown that a non-trivial axion solution is incompatible with a non-trivial (holographic) IR conformal fixed point. Imposing a suitable axion regularity condition allows to select the IR geometry in a unique way. The solutions are found analytically in the asymptotic UV and IR regimes, and it is shown that in those regimes the axion backreaction is always negligible. The axion backreaction may become important in the intermediate region of the bulk. To make contact with the axion probe limit solutions, a systematic expansion of the solution is developed. Several concrete examples are worked out numerically. It is shown that the regularity condition always implies a finite allowed range for the axion source parameter in the UV. This translates into the existence of a finite (but large) number of saddle-points in the large $N_c$ limit. This ties in well with axion-swampland conjectures.
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