IR Behavior Research Articles

Three-field potential for soft-wall AdS/QCD

The Anti-de Sitter Space/Conformal Field Theory (AdS/CFT) correspondence may offer new and useful insights into the non-perturbative regime of strongly coupled gauge theories such as Quantum Chromodynamics (QCD). Soft-wall AdS/QCD models have reproduced the linear Regge trajectories of meson spectra by including background dilaton and chiral condensate fields. Efforts to derive these background fields from a scalar potential have so far been unsuccessful in satisfying the UV boundary conditions set by the AdS/CFT dictionary while reproducing the IR behavior needed to obtain the correct meson spectra. We present work toward a three-field scalar potential that includes the dilaton field and the chiral and glueball condensates. This model is consistent with background fields that yield linear trajectories for the meson spectra and the correct mass-splitting between the vector and axial-vector mesons.

Charge expulsion from black brane horizons, and holographic quantum criticality in the plane

Quantum critical behavior in 2+1 dimensions is established via holographic methods in a 5+1-dimensional Einstein gravity theory with gauge potential form fields of rank 1 and 2. These fields are coupled to one another via a tri-linear Chern-Simons term with strength k. The quantum phase transition is physically driven by the expulsion of the electric charge from inside the black brane horizon to the outside, where it gets carried by the gauge fields which acquire charge thanks to the Chern-Simons interaction. At a critical value k=k_c, zero temperature, and any finite value of the magnetic field, the IR behavior is governed by a near-horizon Lifshitz geometry. The associated dynamical scaling exponent depends on the magnetic field. For k<k_c, the flow towards low temperature is governed by a Reissner-Nordstrom-like black brane whose charge and entropy density are non-vanishing at zero temperature. For k > k_c, the IR flow is towards the purely magnetic brane in AdS_6. Its near-horizon geometry is AdS_4 \times R^2, so that the entropy density vanishes quadratically with temperature, and all charge is carried by the gauge fields outside of the horizon.

The non-SUSY baryonic branch: soft supersymmetry breaking of $ \mathcal{N} = 1 $ gauge theories

We study a non-supersymmetric deformation of the field theory dual to the baryonic branch of Klebanov-Strassler. Using a combination of analytical (series expansions) and numerical methods we construct non-supersymmetric backgrounds that smoothly interpolate between the desired UV and IR behaviors. We calculate various observables of the field theory and propose a picture of soft breaking by gaugino masses that is consistent with the various calculations on the string side.

RG flow of magnetic brane correlators

The magnetic brane solution to five-dimensional Einstein-Maxwell-Chern-Simons theory provides a holographic description of the RG flow from four-dimensional Yang-Mills theory in the presence of a constant magnetic field to a two-dimensional low energy CFT. We compute two-point correlators involving the U(1) current and the stress tensor, and use their leading IR behavior to confirm the existence of a single chiral current algebra, and of left-and right-moving Virasoro algebras in the low energy CFT. The common central charge of the Virasoro algebras is found to match the Brown-Henneaux formula, while the level of the current algebra is related to the Chern-Simons coupling. The coordinate reparametrizations produced by the Virasoro algebras on the AdS3 near-horizon geometry arise from physical non-pure gauge modes in the asymptotic AdS5 region, thereby providing a concrete example for the emergence of IR symmetries. Finally, we interpret the infinite series of sub-leading IR contributions to the correlators in terms of certain double-trace interactions generated by the RG flow in the low energy CFT.

Bimetric renormalization group flows in quantum Einstein gravity

The formulation of an exact functional renormalization group equation for quantum Einstein gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale. The central requirement of “background independence” is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first study of the full-fledged gravitational RG flow, which explicitly accounts for this bimetric structure, by considering an ansatz for the effective average action which includes all three classes of interactions. It is shown that the non-trivial gravitational RG fixed point central to the asymptotic safety program persists upon disentangling the dynamical and background terms. Moreover, upon including the mixed terms, a second non-trivial fixed point emerges, which may control the theory’s IR behavior.

Comments on supercurrent multiplets, supersymmetric field theories and supergravity

We analyze various supersymmetry multiplets containing the supercurrent and the energy-momentum tensor. The most widely known such multiplet, the Ferrara-Zumino (FZ) multiplet, is not always well-defined. This can happen once Fayet-Iliopoulos (FI) terms are present or when the Kähler form of the target space is not exact. We present a new multiplet \( {\mathcal{S}_{\alpha \dot{\alpha }}} \) which always exists. This understanding of the supersymmetry current allows us to obtain new results about the possible IR behavior of supersymmetric theories. Next, we discuss the coupling of rigid supersymmetric theories to supergravity. When the theory has an FZ-multiplet or it has a global R-symmetry the standard formalism can be used. But when this is not the case such simple gauging is impossible. Then, we must gauge the current \( {\mathcal{S}_{\alpha \dot{\alpha }}} \). The resulting theory has, in addition to the graviton and the gravitino, another massless chiral superfield Φ which is essential for the consistency of the theory. Some of the moduli of various string models play the role of Φ. Our general considerations, which are based on the consistency of supergravity, show that such moduli cannot be easily lifted thus leading to constraints on gravity/string models.

Membranes with topological charge andAdS4/CFT3correspondence

If the second Betti number b_2 of a Sasaki-Einstein manifold Y^7 does not vanish, then M-theory on AdS_4 x Y^7 possesses "topological" U(1)^{b_2} gauge symmetry. The corresponding Abelian gauge fields come from three-form fluctuations with one index in AdS_4 and the other two in Y^7. We find black membrane solutions carrying one of these U(1) charges. In the zero temperature limit, our solutions interpolate between AdS_4 x Y^7 in the UV and AdS_2 x R^2 x squashed Y^7 in the IR. In fact, the AdS_2 x R^2 x squashed Y^7 background is by itself a solution of the supergravity equations of motion. These solutions do not appear to preserve any supersymmetry. We search for their possible instabilities and do not find any. We also discuss the meaning of our charged membrane backgrounds in a dual quiver Chern-Simons gauge theory with a global U(1) charge density. Finally, we present a simple analytic solution which has the same IR but different UV behavior. We reduce this solution to type IIA string theory, and perform T-duality to type IIB. The type IIB metric turns out to be a product of the squashed Y^7 and the extremal BTZ black hole. We discuss an interpretation of this type IIB background in terms of the (1+1)-dimensional CFT on D3-branes partially wrapped over the squashed Y^7.

The S-matrix in twistor space

The marvelous simplicity and remarkable hidden symmetries recently uncovered in (Super) Yang-Mills and (Super)Gravity scattering amplitudes strongly suggests the existence of a “weak-weak” dual formulation of these theories where these structures are made more manifest at the expense of manifest locality. In this note we suggest that in four dimensions, this dual description lives in (2, 2) signature and is naturally formulated in twistor space. We begin at tree-level, by recasting the momentum-space BCFW recursion relation in a completely on-shell form that begs to be transformed into twistor space. Our transformation is strongly inspired by Witten’s twistor string theory, but differs in treating twistor and dual twistor variables on a more equal footing; a related transcription of the BCFW formula using only twistor space variables has been carried out independently by Mason and Skinner. Using both twistor and dual twistor variables, the three and four-point amplitudes are strikingly simple–for Yang-Mills theories they are “1” or “-1”. The BCFW computation of higher-order amplitudes can be represented by a simple set of diagrammatic rules, concretely realizing Penrose’s program of relating “twistor diagrams” to scattering amplitudes. More specifically, we give a precise definition of the twistor diagram formalism developed over the past few years by Andrew Hodges. The “Hodges diagram” representation of the BCFW rules allows us to compute amplitudes and study their remarkable properties in twistor space. For instance the diagrams for Yang-Mills theory are topologically disks and not trees, and reveal striking connections between amplitudes that are not manifest in momentum space. Twistor space also suggests a new representation of the amplitudes directly in momentum space, that is naturally determined by the Hodges diagrams. The BCFW rules and Hodges diagrams also enable a systematic twistorial formulation of gravity. All tree amplitudes can be combined into an “S-Matrix” scattering functional which is the natural holographic observable in asymptotically flat space; the BCFW formula turns into a simple quadratic equation for this “S-Matrix” in twistor space, providing a holographic description of \( \mathcal{N} = 4 \) SYM and \( \mathcal{N} = 8 \) Supergravity at tree level. We move on to initiate the exploration of loop amplitudes in (2, 2) signature and twistor space, beginning with a discussion of their IR behavior. We find that the natural pole prescriptions needed for transformation to twistor space make the amplitudes perfectly well-defined objects, free of IR divergences. Indeed in momentum space, the loop amplitudes so regulated vanish for generic momenta, and transformed to twistor space, are even simpler than their tree-level counterparts: the full 4-pt one-loop amplitudes in \( \mathcal{N} = 4 \) SYM are simply equal to “1” or “0”! This further supports the idea that there exists a sharply defined object corresponding to the S-Matrix in (2, 2) signature, computed by a dual theory naturally living in twistor space.

Quark confinement from colour confinement

We relate quark confinement, as measured by the Polyakov-loop order parameter, to colour confinement, as described by the Kugo–Ojima/Gribov–Zwanziger scenario. We identify a simple criterion for quark confinement based on the IR behaviour of ghost and gluon propagators, and compute the order-parameter potential from the knowledge of Landau-gauge correlation functions with the aid of the functional RG. Our approach predicts the deconfinement transition in quenched QCD to be of first order for SU(3) and second order for SU(2) – in agreement with general expectations. As an estimate for the critical temperature, we obtain Tc≃284 MeV for SU(3).

Passive cooling for air-conditioning energy savings with new radiative low-cost coatings

Passive cooling is considered as an alternative technology to avoid unwanted heat gains, to reduce urban heat islands and to generate cooling potential for buildings (limiting air-conditioning energy). According to materials and surface treatments, the roof can represent to be a major heat gain source from opaque elements of the building fabric, heating up the outer surface and increasing heat flow by conduction. This paper presents low-cost new radiative materials (1 ∉/m2) allowing to limit heat gains during diurnal cycle for hot seasons. To evaluate the relevance of these new substrates, their reflective UV–VIS–IR behavior are studied and compared to classical roofed materials available in industrial and developing countries. A 48 m2 experimental roof having different surfaces (plate steel sheets, fiber cement, terra cotta tiles and corrugated sheets) allows to determine the temperature ratio δ between uncoated and coated materials. Up to 34% surface temperature gains are obtained for white coated CS, 25% for FC and ∼18% for TCT and PSS. According to uncoated materials for a surface temperature T0 = 60 °C, simulations showed that the low-cost white opaque reflective roofs (50 m2) presented in this study would reduce cooling energy consumption by 26–49%.

From linear SUSY to constrained superfields

We present a new formalism for finding the low-energy effective Lagrangian of Goldstinos and other fields. This Lagrangian is written using standard superspace and the superfields are constrained to include only the light degrees of freedom. The Goldstino resides in a (constrained) chiral superfield X which is naturally identified at short distances. This allows us to exactly compute the IR behavior of some correlation functions even in strongly coupled theories with SUSY breaking. The Goldstino couplings above the scale of the matter superpartners are determined by identifying X with the standard spurion. At energies below the superpartners' scale, fermions, scalars (including Goldstone bosons) and gauge fields are also described by constrained superfields. Our framework makes it easy to find the leading order terms in the Lagrangian and to control their corrections. It simplifies the derivation of many known results and leads to new ones.

5D dilaton–gravity and gluon plasma thermodynamics

I will describe black–hole solutions in five–dimensional gravity with a self–interacting scalar field. The geometry is asymptotically logarithmically anti–de Sitter in the UV. A phase transition occurs if an only if the IR behavior of the dilaton potential is associated to a confining gauge theory. The transition is holographically dual to the confining/deconfining phase transition of a 4d theory closely matching pure Yang–Mills, both at zero and finite temperature. The trace anomaly equation is reproduced in the gravity picture, as a check of the duality.

Operator product expansion for B-meson distribution amplitude and dimension-5 HQET operators

When the bilocal heavy-quark effective theory (HQET) operator for the B-meson distribution amplitude has a light-like distance t between the quark and antiquark fields, the scale ∼1/t separates the UV and IR regions, which induce the cusp singularity in radiative corrections and the mixing of multiparticle states in nonperturbative corrections, respectively. We treat these notorious UV and IR behaviors simultaneously using the operator product expansion, with the local operators of dimension d⩽5 and radiative corrections at order αs for the corresponding Wilson coefficients. The result is derived in the coordinate space, which manifests the Wilson coefficients with Sudakov-type double logarithms and the higher-dimensional operators with additional gluons. This result yields the B-meson distribution amplitude for t less than ∼1 GeV−1, in terms of Λ¯=mB−mb and the two additional HQET parameters as matrix elements of dimension-5 operators. The impact of these novel HQET parameters on the integral relevant to exclusive B decays, λB, is also discussed.

$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory

By analyzing brane configurations in detail, and extracting general lessons, we develop methods for analyzing S-duality of supersymmetric boundary conditions in N=4 super Yang-Mills theory. In the process, we find that S-duality of boundary conditions is closely related to mirror symmetry of three-dimensional gauge theories, and we analyze the IR behavior of large classes of quiver gauge theories.

Subleading-color contributions to gluon-gluon scattering in 𝒩 = 4 SYM theory and relations to 𝒩 = 8 supergravity

We study the subleading-color (nonplanar) contributions to the four-gluon scattering amplitudes in = 4 supersymmetric SU(N) Yang-Mills theory. Using the formalisms of Catani and of Sterman and Tejeda-Yeomans, we develop explicit expressions for the infrared-divergent contributions of all the subleading-color L-loop amplitudes up to three loops, and make some conjectures for the IR behavior for arbitrary L. We also derive several intriguing relations between the subleading-color one- and two-loop four-gluon amplitudes and the four-graviton amplitudes of = 8 supergravity. The exact one- and two-loop = 8 supergravity amplitudes can be expressed in terms of the one- and two-loop N-independent = 4 SYM amplitudes respectively, but the natural generalization to higher loops fails, despite having a simple interpretation in terms of the 't Hooft picture. We also find that, at least through two loops, the subleading-color amplitudes of = 4 SYM theory have uniform transcendentality (as do the leading-color amplitudes). Moreover, the = 4 SYM Catani operators, which express the IR-divergent contributions of loop amplitudes in terms of lower-loop amplitudes, are also shown to have uniform transcendentality, and to be the maximum transcendentality piece of the QCD Catani operators.

Generalised Unitarity at One-loop with Massive Fermions

We describe an application of generalised unitarity to the computation of one-loop amplitudes with massive external fermions. We present complete results for the leading colour contributions to the all-plus helicity configuration of the tt¯gg amplitude. Using a special choice for the helicity basis for the massive fermions we are able to obtain extremely compact analytic expressions. In particular we describe how one can fix the divergent contributions from tadpole and wave-function renormalisation using universal UV and IR behaviour.

Massive stars exploding in a He-rich circumstellar medium - III. SN 2006jc: infrared echoes from new and old dust in the progenitor CSM

We present near- (NIR) and mid-infrared (MIR) photometric data of the Type Ibn supernova (SN) 2006jc obtained with the United Kingdom Infrared Telescope (UKIRT), the Gemini North Telescope and the Spitzer Space Telescope between days 86 and 493 post-explosion. We find that the IR behaviour of SN 2006jc can be explained as a combination of IR echoes from two manifestations of circumstellar material. The bulk of the NIR emission arises from an IR echo from newly condensed dust in a cool dense shell (CDS) produced by the interaction of the ejecta outward shock with a dense shell of circumstellar material ejected by the progenitor in a luminous blue variable (LBV)-like outburst about two years prior to the SN explosion. The CDS dust mass reaches a modest 3.0 × 10^(−4) M_⊙ by day 230. While dust condensation within a CDS formed behind the ejecta inward shock has been proposed before for one event (SN 1998S), SN 2006jc is the first one showing evidence for dust condensation in a CDS formed behind the ejecta outward shock in the circumstellar material. At later epochs, a substantial and growing contribution to the IR fluxes arises from an IR echo from pre-existing dust in the progenitor wind. The mass of the pre-existing circumstellar medium (CSM) dust is at least ∼8 × 10^(−3) M_⊙. This paper therefore adds to the evidence that mass-loss from the progenitors of core-collapse SNe could be a major source of dust in the Universe. However, yet again, we see no direct evidence that the explosion of an SN produces anything other than a very modest amount of dust.

Gauge/gravity duality and the interplay of various fractional branes

We consider different types of fractional branes on a Z{sub 2} orbifold of the conifold and analyze in detail the corresponding gauge/gravity duality. The gauge theory possesses a rich and varied dynamics, both in the UV and in the IR. We find the dual supergravity solution, which contains both untwisted and twisted 3-form fluxes, related to what are known as deformation and N=2 fractional branes, respectively. We analyze the resulting renormalization group flow from the supergravity perspective, by developing an algorithm to easily extract it. We find hints of a generalization of the familiar cascade of Seiberg dualities due to a nontrivial interplay between the different types of fractional branes. We finally consider the IR behavior in several limits, where the dominant effective dynamics is either confining in a Coulomb phase or runaway, and discuss the resolution of singularities in the dual geometric background.

Two-loop graviton scattering relation and IR behavior in [formula omitted] supergravity

We derive an ABDK-like relation between the one- and two-loop four-graviton amplitudes in N = 8 supergravity. Specifically we show that the infrared-divergent part of the two-loop amplitude is one-half the square of the one-loop amplitude, suggesting an exponential structure for IR divergences. The difference between the two-loop amplitude and one-half the square of the full one-loop amplitude is therefore finite, and expressible in a relatively simple form. We give arguments for generalizations to higher loops and n-point functions, suggesting that the exponential of the full one-loop amplitude may be corrected, to low orders, by only simple finite terms.

A vector supersymmetry killing IR divergences in non-commutative gauge theories

This is a report on the joint work with François Gieres, Stefan Hohenegger, Olivier Piguet and Manfred Schweda. We consider a non-commutative U(1) gauge theory with an extension which was originally proposed by A. A. Slavnov [3, 4] in order to get rid of UV/IR mixing problems. Here we show, that the improved IR behaviour of this model is mainly due to the appearence of a linear vector supersymmetry.