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Abstract We investigate the global structure of the recently discovered family of SL(2,ℤ)-invariant potentials describing inflationary α-attractors. These potentials have an inflationary plateau consisting of the fundamental domain and its images fully covering the upper part of the Poincaré half-plane. Meanwhile, the lower part of the half-plane is covered by an infinitely large number of ridges, which, at first glance, are too sharp to support inflation. However, we show that this apparent sharpness is just an illusion created by hyperbolic geometry, and each of these ridges is physically equivalent to the inflationary plateau in the upper part of the Poincaré half-plane. 

Abstract We study cosmological theory where the kinetic term and potential have SL(2,ℤ) symmetry. Potentials have a plateau at large values of the inflaton field, where the axion forms a flat direction. Due to the underlying hyperbolic geometry and special features of SL(2,ℤ) potentials, the theory exhibits an α-attractor behavior: its cosmological predictions are stable with respect to significant modifications of the SL(2,ℤ) invariant potentials. We present a supersymmetric version of this theory in the framework ofD3 induced geometric inflation. The choice ofαis determined by underlying string compactification. For example, in a CY compactification withT², one has 3α= 1, the lowest discrete Poincaré disk target for LiteBIRD. 

A<sc>bstract</sc> Millicharged particles are generic in theories of dark sectors. A cosmic or local abundance of them may be produced by the early universe, stellar environments, or the decay or annihilation of dark matter/dark energy. Furthermore, if such particles are light, these production channels result in a background of millicharged radiation. We show that light-shining-through-wall experiments employing superconducting RF cavities can also be used as “direct deflection” experiments to search for this relativistic background. The millicharged plasma is first subjected to an oscillating electromagnetic field of a driven cavity, which causes charge separation in the form of charge and current perturbations. In turn, these perturbations can propagate outwards and resonantly excite electromagnetic fields in a well-shielded cavity placed nearby, enabling detection. We estimate that future versions of the existing Dark SRF experiment can probe orders of magnitude of currently unexplored parameter space, including millicharges produced from the Sun, the cosmic neutrino background, or other mechanisms that generate a thermal abundance with energy density as small as ~ 10⁻⁴that of the cosmic microwave background. 

Abstract Dark matter's existence is known thanks to its gravitational interaction with Standard Model particles, but it remains unknown whether this is the only force present between them. While many searches for such new interactions with dark matter focus on short-range, contact-like interactions, it is also possible that there exist weak, long-ranged forces between dark matter and the Standard Model. In this work, we present two types of constraints on such new interactions. First, we consider constraints arising from the fact that such a force would also induce long range interactions between Standard Model particles themselves, as well as between dark matter particles themselves. Combining the constraints on these individual forces generally sets the strongest constraints available on new Standard Model-dark matter interactions. Second, we consider the possibility of constraining new long-ranged interactions between dark matter and the Standard Model using the effects of dynamical friction in ultrafaint dwarf galaxies, especially Segue I. Such new interactions would accelerate the transfer of kinetic energy from stars to their surrounding dark matter, slowly reducing their orbits; the present-day stellar half-light radius of Segue I therefore allows us to exclude new forces which would have reduced stars' orbital radii below this scale by now. 

A<sc>bstract</sc> The D0-brane/Banks-Fischler-Shenker-Susskind matrix theory is a strongly coupled quantum system with an interesting gravity dual. We develop a scheme to derive bootstrap bounds on simple correlators in the matrix theory at infiniteNat zero energy by imposing the supercharge equations of motion. By exploiting SO(9) symmetry, we are able to consider single-trace operators involving words of length up to 9 using very modest computational resources. We interpret our initial results as strong evidence that the bootstrap method can efficiently access physics in the strongly coupled, infiniteNregime. 

A<sc>bstract</sc> We discuss known maximalD-dimensional supergravities of two types: type I withG/Hcoset spaces and type II derived by compactification from higher dimensions without dualization, these have less manifest symmetries. In 4Dand 6Din type I models we perform explicit gauge-fixing of localHsymmetries in unitary gauges: symmetric, Iwasawa and partial Iwasawa. In 4Dsupergravity I in symmetric gauge globalH-invariance and nonlinearly realizedG-symmetry are valid on shell, classically. The globalH-symmetry andG-symmetry in Iwasawa-type gauges in type I and in type II supergravities are not manifest, if at all present. This fact raises the issue of the gauge equivalence of the S-matrix of various gauge-fixedD-dimensional supergravities and its relation to the ones computable using superamplitude methods. 

A<sc>bstract</sc> Recent research has leveraged the tractability of$$ T\overline{T} $$ $T\overline{T}$style deformations to formulate timelike-bounded patches of three-dimensional bulk spacetimes includingdS₃. This proceeds by breaking the problem into two parts: a solvable theory that captures the most entropic energy bands, and a tuning algorithm to treat additional effects and fine structure. We point out that the method extends readily to higher dimensions, and in particular does not require factorization of the fullT²operator (the higher dimensional analogue of$$ T\overline{T} $$ $T\overline{T}$defined in [1]). Focusing ondS₄, we first define a solvable theory at finiteNvia a restrictedT²deformation of theCFT₃onS²×ℝ, in whichTis replaced by the form it would take in symmetric homogeneous states, containing only diagonal energy densityE/Vand pressure (-dE/dV) components. This explicitly defines a finite-N solvable sector ofdS₄/deformed-CFT₃, capturing the radial geometry and count of the entropically dominant energy band, reproducing the Gibbons-Hawking entropy as a state count. To accurately capture local bulk excitations ofdS₄including gravitons, we build a deformation algorithm in direct analogy to the case ofdS₃with bulk matter recently proposed in [2]. This starts with an infinitesimal stint of the solvable deformation as a regulator. The full microscopic theory is built by adding renormalized versions ofT²and other operators at each step, defined by matching to bulk local calculations when they apply, including an uplift fromAdS₄/CFT₃todS₄(as is available in hyperbolic compactifications of M theory). The details of the bulk-local algorithm depend on the choice of boundary conditions; we summarize the status of these in GR and beyond, illustrating our method for the case of the cylindrical Dirichlet condition which can be UV completed by our finite quantum theory. 

A<sc>bstract</sc> We introduce Ward identities for superamplitudes inD-dimensional$$ \mathcal{N} $$ $N$-extended supergravities. These identities help to clarify the relation between linearized superinvariants and superamplitudes. The solutions of these Ward identities for ann-partice superamplitude take a simple universal form for half BPS and non-BPS amplitudes. These solutions involve arbitrary functions of spinor helicity and Grassmann variables for each of thensuperparticles. The dimension of these functions at a given loop order is exactly the same as the dimension of the relevant superspace Lagrangians depending on half-BPS or non-BPS superfields, given by (D− 2)L+ 2 −$$ \mathcal{N} $$ $N$or (D− 2)L+ 2 −$$ 2\mathcal{N} $$ $2N$, respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree. 

A<sc>bstract</sc> For the Laplacian of ann-Riemannian manifoldX, the Weyl law states that thek-th eigenvalue is asymptotically proportional to (k/V)^2/n, whereVis the volume ofX. We show that this result can be derived via physical considerations by demanding that the gravitational potential for a compactification onXbehaves in the expected (4+n)-dimensional way at short distances. In simple product compactifications, when particle motion onXis ergodic, for largekthe eigenfunctions oscillate around a constant, and the argument is relatively straightforward. The Weyl law thus allows to reconstruct the four-dimensional Planck mass from the asymptotics of the masses of the spin 2 Kaluza-Klein modes. For warped compactifications, a puzzle appears: the Weyl law still depends on the ordinary volumeV, while the Planck mass famously depends on a weighted volume obtained as an integral of the warping function. We resolve this tension by arguing that in the ergodic case the eigenfunctions oscillate now around a power of the warping function rather than around a constant, a property that we callweighted quantum ergodicity. This has implications for the problem of gravity localization, which we discuss. We show that for spaces with Dp-brane singularities the spectrum is discrete only forp= 6,7,8, and for these cases we rigorously prove the Weyl law by applying modern techniques from RCD theory. 

A<sc>bstract</sc> A feature the$$ \mathcal{N} $$ $N$= 2 supersymmetric Sachdev-Ye-Kitaev (SYK) model shares with extremal black holes is an exponentially large number of ground states that preserve supersymmetry. In fact, the dimension of the ground state subsector is a finite fraction of the total dimension of the SYK Hilbert space. This fraction has a remarkably simple bulk interpretation as the probability that the zero-temperature wormhole — a supersymmetric Einstein-Rosen bridge — has vanishing length. Using chord techniques, we compute the zero-temperature Hartle-Hawking wavefunction; the results reproduce the ground state count obtained from boundary index computations, including non-perturbative corrections. Along the way, we improve the construction [1] of the super-chord Hilbert space and show that the transfer matrix of the empty wormhole enjoys an enhanced$$ \mathcal{N} $$ $N$= 4 supersymmetry. We also obtain expressions for various two point functions at zero temperature. Finally, we find the expressions for the supercharges acting on more general wormholes with matter and present the superchord algebra.