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Li-Yuan Chiang

Publications and source records attributed to Li-Yuan Chiang.

9 recordsLinked to original sources
arXiv2026

Moments in the CFT Landscape

We develop a novel numerical bootstrap for unitary, crossing-symmetric conformal field theories, focusing on moment observables defined as weighted averages over conformal data. Providing a global and coarse-grained probe of the operator spectrum, this framework yields numerically rigorous bounds on the operator distribution using standard semidefinite programming techniques. In the heavy correlator regime, these bounds remain robust and converge rapidly towards analytically-derived power laws. At finite external dimensions, low-lying moments capture corrections to analytic heavy limit results, while reproducing familiar bootstrap solutions such as Ising-model kinks on the boundary of moment space. Most importantly, the moment bootstrap reveals new features in previously unexplored regions of the bootstrap landscape. The lower bounds on moment variables exhibit two continuous families of kinks persisting across $2 < d < 6$, reflecting nontrivial spectral reorganizations connected to underlying operator decoupling phenomena. These results demonstrate that moment variables uncover bootstrap solutions and collective structures that are difficult to access within traditional numerical approaches.

hep-th↗
arXiv2025

Ultralow-V{\pi}L Silicon Electro-Optic Directional Coupler Switch with a Liquid Crystal Cladding

An ultralow-V{\pi}L photonic switch device is demonstrated utilizing the high optical and electrical field confinement in silicon slot waveguides coupled with the strong electro-optic response of nematic liquid crystals. A silicon photonic directional coupler switch with a modulation efficiency of 0.0195 Vmm and a loss-efficiency product of 0.0624 VdB is achieved. The 1.5 mm long device is based on two-mode interference within a single slot waveguide resulting in a V{\pi} of 0.013 V and an extinction ratio of ~ 9dB at 1550 nm wavelength. The power consumption of the photonic switch is estimated to be below 0.6 nW and it possesses a response time of <1.5 ms. A comparative performance study between the directional coupler switch and a Mach-Zehnder Interferometer (MZI) switch is performed. The directional coupler switch is projected to have a smaller footprint and lower optical loss compared to a similar design MZI switch making it a strong candidate for switch matrix designs and applications.

physics.optics↗
arXiv2023

Bootstrapping string theory EFT

We study the space of open string effective field theories by combining the constraint of unitarity and monodromy relations for the four-point amplitude. The latter is a reflection of an underlying disk correlator with singularities at the boundary. By assuming maximal susy the resulting bootstrap isolates Wilson coefficients to at least $10^{-4}$ of the Type-I superstring. Furthermore, utilizing our geometric approach, we obtain the critical dimension of 10 from the low energy coefficients alone. Remarkably, relaxing SUSY but requiring the massless states to carry four-dimensional helicities, the Wilson coefficients are again constrained to superstring values within $10^{-4}$. Thus we conclude that type-I string theory is the unique solution to the monodromy bootstrap with either maximal susy or vector external states. We also introduce Tachyons to the bootstrap and demonstrate for the scattering of external vectors, the bosonic and superstring span the allowed region. Allowed regions for closed string effective field theories are obtained by implementing the KLT relations.

hep-th↗
arXiv2023

The Geometry of the Modular Bootstrap

We explore the geometry behind the modular bootstrap and its image in the space of Taylor coefficients of the torus partition function. In the first part, we identify the geometry as an intersection of planes with the convex hull of moment curves on $R^+{\otimes}\mathbb{Z}$, with boundaries characterized by the total positivity of generalized Hankel matrices. We phrase the Hankel constraints as a semi-definite program, which has several advantages, such as constant computation time with increasing central charge. We derive bounds on the gap, twist-gap, and the space of Taylor coefficients themselves. We find that if the gap is above $\Delta^*_{gap}$, where $\frac{c{-}1}{12}<\Delta^*_{gap}< \frac{c}{12}$, all coefficients become bounded on both sides and kinks develop in the space. In the second part, we propose an analytic method of imposing the integrality condition for the degeneracy number in the spinless bootstrap, which leads to a non-convex geometry. We find that even at very low derivative order this condition rules out regions otherwise allowed by bootstraps at high derivative order.

hep-th↗
arXiv2022

Silicon-organic hybrid thermo-optic switch based on a slot waveguide directional coupler

We propose and demonstrate a passively biased 2 by 2 thermo-optic switch with high power efficiency and fast response time. The device benefits from the highly concentrated optical field of a slot waveguide mode and the strong thermo-optic effect of a nematic liquid crystal (NLC) cladding. The NLC fills the nano-slot region and is aligned by the subwavelength grating inside. The measured power consumption and thermal time constant are 0.58 mW and 11.8 microsecond, respectively, corresponding to a figure-of-merit of 6.8. The proposed silicon-organic hybrid device provides a new solution to design thermo-optic actuators having lower power consumption and fast operation speed.

physics.optics↗
arXiv2022

De-projecting the EFThedron

The space of Wilson coefficients of EFT that can be UV completed into consistent theories was recently shown to be described analytically by a positive geometry, termed the EFThedron. However, this geometry, as well as complementary numerical methods of semi-definite programming, have so far focused on the positivity of the partial wave expansion, which allows bounding only ratios of couplings. In this paper we describe how the unitarity upper bound of the partial waves can be incorporated. This new problem can be formulated in terms of the well known $L$-moment problem, which we generalize and solve from a geometrical perspective. We find the non-projective generalization of the EFThedron has an infinite number of non-linear facets, which in some cases have remarkably simple descriptions. We use these results to derive bounds on single couplings, finding that the leading derivative operators are bounded by unity, when normalized by the cut-off scale and loop factors. For general operators of mass dimension $2k$ we find the upper bound is heavily suppressed at large $k$, with an $1/k$ fall-off.

hep-th↗
arXiv2022

(Non)-projective bounds on gravitational EFT

In this paper we study both projective and non-projective constraints on four-dimensional gravitational effective fields theories implied from unitarity, causality and crossing, assuming perturbative UV completions in $M_{\rm pl}$. We derive bounds on the Wilson coefficients of $R^3$ and $D^{2n}R^4$ from its dispersive representation, utilizing both numerical semi-definite programming and analytic geometry analysis. From the former, we derive projective bounds on ratios of couplings and observe accumulation point spectrum populating the boundary of the allowed region. For the latter we consider the non-projective geometry of the EFThedron, which we relate to the known $L$-moment problem in the literature. This allows us to move beyond positivity and incorporate the upper bound from unitarity of the imaginary parts of partial waves. This leads to sharp bounds on individual coefficients, which are of order unity when normalized with respect to the UV scale. Finally, the non-projective geometry also allows us to derive optimal bounds reflecting assumptions of low-spin dominance, improving previous results. We complement the analytic analysis with a simple linear programming approach that validates the bounds.

hep-th↗
arXiv2021

Into the EFThedron and UV constraints from IR consistency

Recently it was proposed that the theory space of effective field theories with consistent UV completions can be described as a positive geometry, termed the EFThedron. In this paper we demonstrate that at the core, the geometry is given by the convex hull of the product of two moment curves. This makes contact with the well studied bi-variate moment problem, which in various instances has known solutions, generalizing the Hankel matrices of couplings into moment matrices. We are thus able to obtain analytic expressions for bounds, which perfectly match numerical results from semi-definite programing methods. Furthermore, we demonstrate that crossing symmetry in the IR imposes non-trivial constraints on the UV spectrum. In particular, permutation invariance for identical scalar scattering requires that any UV completion beyond the scalar sector must contain arbitrarily high spins, including at least all even spins $\ell\le28$, with the ratio of spinning spectral functions bounded from above, exhibiting large spin suppression. The spinning spectrum must also include at least one state satisfying a bound $m^2_{J}<M^2 \frac{( J^2-12) ( J^4 - 32 J^2 +204)}{8 (150 - 43 J^2 + 2 J^4)}$, where $J^2=\ell(\ell+1)$, and $M^2$ is the mass of the heaviest spin 2 state in the spectrum.

hep-th↗