Superconformal symmetry, supergravity and cosmology

We study implications of $$ \mathcal{N}=4 $$ superconformal symmetry in three dimensions, thus extending our earlier results in [1] devoted to the $$ \mathcal{N}\le 3 $$ cases. We show that the three-point function of the supercurrent in $$ \mathcal{N}=4 $$ superconformal field theories contains two linearly independent forms. However, only one of these structures contributes to the three-point function of the energy-momentum tensor and the other one is present in those $$ \mathcal{N}=4 $$ superconformal theories which are not invariant under the mirror map. We point out that general $$ \mathcal{N}=4 $$ superconformal field theories admit two inequivalent flavour current multiplets and show that the three-point function of each of them is determined by one tensor structure. As an example, we compute the two- and three-point functions of the conserved currents in $$ \mathcal{N}=4 $$ superconformal models of free hypermultiplets. We also derive the universal relations between the coefficients appearing in the two- and threepoint correlators of the supercurrent and flavour current multiplets in all superconformal theories with $$ \mathcal{N}\le 4 $$ supersymmetry. Our derivation is based on the use of Ward identities in conjunction with superspace reduction techniques.

▪ Abstract The evolution of the universe is the ultimate laboratory for studying fundamental physics across energy scales that span approximately 25 orders of magnitude. The standard models of cosmology and particle physics provide the basic understanding of the early and present universe and predict a series of phase transitions that occurred in succession during the universe's expansion and cooling history. We survey these phase transitions, highlighting the equilibrium and nonequilibrium effects as well as their observational and cosmological consequences. We discuss the current theoretical and experimental programs studying phase transitions in QCD and nuclear matter in accelerators. A critical assessment of similarities and differences between the conditions in the early universe and those in ultrarelativistic heavy ion collisions is presented. Cosmological observations and accelerator experiments are converging toward an unprecedented understanding of the early and present universe.

Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on numerous extensions of the correspondence up to early 2020. This is an extended writeup of the lectures given at the Winter School ‘YRISW 2020’ to appear in a special issue of J. Phys. A. Class S is a wide class of 4d N=2 supersymmetric gauge theories (ranging from super-QCD (quantum chromodynamics) to non-Lagrangian theories) obtained by twisted compactification of 6d N=(2,0) superconformal theories on a Riemann surface C. This 6d construction yields the Coulomb branch and Seiberg–Witten geometry of class S theories, geometrizes S-duality, and leads to the AGT correspondence, which states that many observables of class S theories are equal to 2d conformal field theory (CFT) correlators. For instance, the four-sphere partition function of a 4d N=2SU(2) superconformal quiver theory is equal to a Liouville CFT correlator of primary operators. Extensions of the AGT correspondence abound: asymptotically-free gauge theories and Argyres–Douglas theories correspond to irregular CFT operators, quivers with higher-rank gauge groups and non-Lagrangian tinkertoys such as T N correspond to Toda CFT correlators, and nonlocal operators (Wilson–’t Hooft loops, surface operators, domain walls) correspond to Verlinde networks, degenerate primary operators, braiding and fusion kernels, and Riemann surfaces with boundaries.

We consider gauge vortices in symmetry-breaking models with a noncanonical kinetic term. This work extends our previous study on global topological $k$-defects [Phys. Rev. D 74, 085004 (2006), including a gauge field. The model consists of a scalar field with a noncanonical kinetic term, while for the gauge field the standard form of its kinetic term is preserved. Topological defects arising in such models, $k$-vortices, may have quite different properties as compared to standard vortices. This happens because an additional dimensional parameter enters the Lagrangian for the considered model---a kinetic mass. We briefly discuss possible consequences for cosmology, in particular, the formation of cosmic strings during phase transitions in the early universe and their properties.

We show that there are two supersymmetric completions of the three-dimensional Chern-Simons theory of level k with gauge group U(N)xU(N) coupled to four sets of massless scalars and spinors in the bi-fundamental representation, if we require Sp(2) global symmetry with the matter fields in the fundamental representation of SU(4). One is the N=6 superconformal theory recently studied in arXiv:0806.1218 [hep-th] and another is a new theory with N=1 superconformal symmetry. We conjecture that the N=1 theory is dual to M theory on AdS_4 x Squashed S^7/Z_k.

N = 4 superconformal coset theories

We study the (2,0) superconformal theories in six dimensions, which arise from the low-energy limit of k coincident 5-branes, using their discrete light-cone formulation as a superconformal quantum mechanical sigma model. We analyze the realization of the superconformal symmetry in the quantum mechanics, and the realization of primary operators. As an example we compute the spectrum of chiral primary states in symmetric Spin(5)_R representations. To facilitate the analysis we introduce and briefly discuss a new class of Lorentz non-invariant theories, which flow in the IR to the (2,0) superconformal field theories but differ from them in the UV.

The Peccei-Quinn solution to the strong CP problem provides a motivated framework rich in cosmological consequence. Thermal axion production is unavoidable if there is a thermal bath at early times. Scattering and decay processes of bath particles can dump relativistic axions in the primordial plasma, and they can leave observable signatures in cosmological observables probing both the early and the late universe if produced with a significant abundance. We present recent and significant improvements for the calculation of the axion production rate for different scenarios and apply these results to predict the abundance of produced axions. Finally, we provide updated cosmological bounds on the QCD axion mass.

Cosmic strings and domain walls

The chiral primary operators of the D=6 superconformal (2,0) theory corresponding to 14 scalars of N=4 D=7 supergravity are obtained by expanding the world volume action for the M5-brane around an AdS_7 x S^4 background. In the leading order, the operators take their values in the symmetric traceless representation of the SO(5) R-symmetry group in consistency with the early conjecture on their structure based on the superconformal symmetry and Matrix-like model arguments.

I explore the observational consequences of resonant particle production during inflation, focusing on its impact on dark matter annihilation signals today. A transient burst of particle production generates localized features in the primordial power spectrum, enhancing the formation of compact small-scale dark matter structures known as prompt cusps. If dark matter consists of thermal weakly interacting massive particles, the resulting small-scale structures substantially boost annihilation rates, leaving potentially detectable imprints in gamma-ray observations. Using 15 years of Fermi Large Area Telescope data targeting the Virgo cluster, I derive upper limits on the thermally averaged annihilation cross section <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo stretchy="false">⟨</a:mo> <a:mi>σ</a:mi> <a:mi>v</a:mi> <a:mo stretchy="false">⟩</a:mo> </a:math> , connecting inflationary particle production in the early Universe with present-day observations constraining dark matter annihilation.

Evolution equation for the expectation value of a scalar field in spatially flat RW universes

Cosmological implications of axinos

We study quantum effects on moduli dynamics arising from the production of particles which are light at points of enhanced symmetry in moduli space. The resulting forces trap the moduli at these points. Moduli trapping occurs in time-dependent quantum field theory, as well as in systems of moving D-branes, where it leads the branes to combine into stacks. Trapping also occurs in the presence of gravity, though the range over which the moduli can roll is limited by Hubble friction. We observe that a scalar field trapped on a steep potential can induce a stage of acceleration of the universe, which we call trapped inflation. Moduli trapping ameliorates the cosmological moduli problem and may affect vacuum selection. In particular, rolling moduli are most powerfully attracted to the points of greatest symmetry. Given suitable assumptions about the dynamics of the very early universe, this effect might help to explain why among the plethora of possible vacuum states of string theory, we appear to live in one with a large number of (spontaneously broken) symmetries.

Theories with elementary scalar degrees of freedom seem nowadays required for simple descriptions of the Standard Model and of the Early Universe. It is then natural to embed theories of inflation in supergravity, also in view of their possible ultraviolet completion in String Theory. After some general remarks on inflation in supergravity, we describe examples of minimal inflaton dynamics which are compatible with recent observations, including higher–curvature ones inspired by the Starobinsky model. We also discuss different scenarios for supersymmetry breaking during and after inflation, which include a revived role for non– linear realizations. In this spirit, we conclude with a discussion of the link, in four dimensions, between “brane supersymmetry breaking” and the super–Higgs effect in supergravity.