Complete EFT Operator Bases for Dark Matter and Weakly-Interacting Light Particle

The standard model can be extended to include weakly-interacting light particle (WILP): real or complex singlet scalar, Majorana or Dirac neutral fermion, neutral or hidden-charged vector boson, etc. Imposing the $Z_2$ symmetry, these particles can be lifted as the weakly-interacting massive particle (WIMP), the candidate of dark matter. Instead, imposing the shift symmetry on the scalar components gives rise to the axion-like particle, dark photon, etc. Utilizing these light degree of freedom along with the standard model particles and imposing different symmetries, we construct the complete and independent sets of effective operators up to dimension eight with the Young tensor technique, consistent with counting from the Hilbert series.Comment: 109 pages. arXiv admin note: text overlap with arXiv:2305.1677

TT‾T\overline{T} deformation in SCFTs and integrable supersymmetric theories

We calculate the $\mathcal{S}$-multiplets for two-dimensional Euclidean $\mathcal{N}=(0,2)$ and $\mathcal{N} = (2,2)$ superconformal field theories under the $T\overline{T}$ deformation at leading order of perturbation theory in the deformation coupling. Then, from these $\mathcal{N} = (0, 2)$ deformed multiplets, we calculate two- and three-point correlators. We show the $\mathcal{N} = (0,2)$ chiral ring's elements do not flow under the $T\overline{T}$ deformation. For the case of $\mathcal{N} = (2,2)$, we show the twisted chiral ring and chiral ring cease to exist simultaneously. Specializing to integrable supersymmetric seed theories, such as $\mathcal{N} = (2,2)$ Landau-Ginzburg models, we use the thermodynamic Bethe ansatz to study the S-matrices and ground state energies. From both an S-matrix perspective and Melzer's folding prescription, we show that the deformed ground state energy obeys the inviscid Burgers' equation. Finally, we show that several indices independent of $D$-term perturbations including the Witten index, Cecotti-Fendley-Intriligator-Vafa index and elliptic genus do not flow under the $T\overline{T}$ deformation.Comment: 46 page

Towards α′\alpha'-finiteness: qq-deformed open string amplitude

Revisiting the Coon amplitude, a deformation of the Veneziano amplitude with a logarithmic generalization of linear Regge trajectories, we scrutinize its potential origins in a worldsheet theory by proposing a definition of its $q$-deformation through the integral representation of the $q$-beta function. By utilizing $q$-deformed commutation relations and vertex operators, we derive the Coon amplitude within the framework of the dual resonance model. We extend this to the open-string context by $q$-deforming the Lie algebra $\mathfrak{su}(1,1)$, resulting in a well-defined $q$-deformed open superstring amplitude. We further demonstrate that the $q$-prefactor in the Coon amplitude arises naturally from the property of the $q$-integral. Furthermore, we find that two different types of $q$-prefactors, corresponding to different representations of the same scattering amplitude, are essentially the same by leveraging the properties of $q$-numbers. Our findings indicate that the $q$-deformed string amplitude defines a continuous family of amplitudes, illustrating how string amplitudes with a finite $\alpha^\prime$ uniquely flow to the amplitudes of scalar scattering in field theory at energy scale $\Lambda$ as $q$ changes from $1$ to $0$. This happens without the requirement of an $\alpha^\prime$ expansion, presenting a fresh perspective on the connection between string and field theories

The Photon Sphere and the AdS/CFT Correspondence

By rephrasing the radial Klein--Gordon equation for a scalar field on anti-de Sitter (AdS) Schwarzschild black hole background in terms of an auxiliary field that satisfies a Schrodinger equation, we demonstrate that the properties of the photon sphere play an important role in the AdS/CFT correspondence. Most importantly, we use constraints imposed by the UV cutoff to derive a highly precise formula describing how a black hole in the bulk amplifies or attenuates an oscillating source dual to boundary operators across the bulk. This formula leads us to identify a phase transition that traps massless fields, which correspond to scalar sources for dual boundary operators, outside the photon sphere when their angular momenta are large enough for classical particles with a matching impact parameter to travel between boundary points. We then use similar reasoning to determine an approximate analytic formula for the QNMs of small black holes at large $l$. The condition for a signal/source to pierce the potential barrier peaking at the photon sphere is, roughly, that its frequency must be greater than the angular momentum of its driven operator times the square of the Lyapunov exponent of the unstable null geodesics.Comment: 33 pages, 7 figure

The Photon Sphere and Response Functions in Holography

Here we follow up on previous work that identified a phase transition in massless scalar fields with the short-lived excitations of an AdS$_4$-Schwarzschild black hole at large angular momenta. In this letter, we show the Unruh temperature of the photon sphere can be determined holographically from the retarded Green's function and is proportional to its circumference according to a boundary observer. We then sharpen the conjecture that the photon sphere, as seen by a boundary observer, is the spatial Fourier transform of the response function. The conjecture is found to be in excellent agreement with our numerics after certain long-lived excitations -- associated with geodesics traveling between boundary points, as predicted by Festuccia and Liu -- are removed from the response, which is then controlled by the short-lived excitations of the AdS black hole.Comment: 6 pages, 5 figure

Hilbert Series and Operator Counting on the Higgs Effective Field Theory

We present a systematic procedure for determining the Hilbert series that counts the number of independent operators in the Higgs effective field theory. After removing the redundancies from equation-of-motion and integration-by-part, we provide an algorithm of treating the redundancy from the operators involving in spurion fields parametrizing the custodial symmetry breaking. Furthermore, we utilize the outer automorphism of the Lorentz and internal symmetries to separate operators with different CP properties. With these new implements, the Hilbert series up to chiral dimension 10 are obtained, and CP-even and CP-odd operators can be further divided. Extensions to all orders are straightforward.Comment: 28 pages, 3 figures, 6 table

Complete NLO Operators in the Higgs Effective Field Theory

We enumerate the complete and independent sets of operators at the next-to-leading order (NLO) in the Higgs effective field theory (HEFT), based on the Young tensor technique on the Lorentz, gauge and flavor structures. The operator-amplitude correspondence tells a type of operators forms the on-shell amplitude basis, and for operators involving in Nambu-Goldstone bosons, the amplitude basis is further reduced to the subspace satisfying the Adler's zero condition in the soft momentum limit. Different from dynamical field, the spurion should not enter into the Lorentz sector, instead it only plays a role of forming the $SU(2)$ invariant together with other dynamical fields. With these new treatments, for the first time we could obtain the 237 (8595) operators for one (three) generation fermions, 295 (11307) with right-handed neutrinos, and find there were 6 (9) terms of operators missing and many redundant operators can be removed in the effective theory without (with) right-handed neutrinos.Comment: 63 pages, 2 tables, revised version: operators in 4-component notation, correct typo for countin