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Fitzpatrick, A. Liam

Publications and source records attributed to Fitzpatrick, A. Liam.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Improving modular bootstrap bounds with integrality

We propose methods that efficiently impose integrality — i.e., the condition that the coefficients of characters in the partition function must be integers — into numerical modular bootstrap. We demonstrate the method with a number of examples where it can be used to strengthen modular bootstrap results. First, we show that, with a mild extra assumption, imposing integrality improves the bound on the maximal allowed gap in dimensions of operators in theories with a U(1) c symmetry at c = 3, and reduces it to the value saturated by the SU(4) 1 WZW model point of c = 3 Narain lattices moduli space. Second, we show that our method can be used to eliminate all but a discrete set of points saturating the bound from previous Virasoro modular bootstrap results. Finally, when central charge is close to 1, we can slightly improve the upper bound on the scaling dimension gap.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Higher d Eisenstein series and a duality-invariant distance measure

The Petersson inner product is a natural inner product on the space of modular invariant functions. We derive a formula, written as a convergent sum over elementary functions, for the inner product E s (G, B) of the real analytic Eisenstein series E s ($τ$, $\overline{τ}$) and a general point in Narain moduli space. We also discuss the utility of the Petersson inner product as a distance measure on the space of 2d CFTs, and apply our procedure to evaluate this distance in various examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Chiral limit of 2d QCD revisited with lightcone conformal truncation

We study the chiral limit of 2d QCD with a single quark flavor at finite Nc using LCT. By modifying the LCT basis according to the quark mass in a manner motivated by ’t Hooft’s analysis, we are able to restore convergence for quark masses much smaller than the QCD strong coupling scale. For such small quark masses, the IR of the theory is expected to be well described by the Sine-Gordon model. We verify that LCT numerics are able to capture in detail the spectrum and correlation functions of the Sine-Gordon model. This opens up the possibility for studying deformations of various integrable CFTs using LCT by considering the chiral limit of QCD like theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Nonperturbative bounds on scattering of massive scalar particles in d ≥ 2

We study two-to-two scattering amplitudes of a scalar particle of mass m. For simplicity, we assume the presence of Z 2 symmetry and that the particle is Z 2 odd. We consider two classes of amplitudes: the fully nonperturbative ones and effective field theory (EFT) ones with a cut-off scale M. Using the primal numerical method which allows us to impose full non-linear unitarity, we construct novel bounds on various observables in 2 ≤ d ≤ 4 space-time dimensions for both classes of amplitudes. We show that our bounds are much stronger than the ones obtained by using linearized unitarity or positivity only. We discuss applications of our bounds to constraining EFTs. Finally, we compare our bounds to the amplitude in Φ 4 theory computed perturbatively at weak coupling, and find that they saturate the bounds.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Form factors and spectral densities from Lightcone Conformal Truncation

We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators $\mathcal{O}$ in $\phi^4$ theory in two dimensions. We show how to use the Hamiltonian eigenstates from LCT to obtain form factors that are matrix elements of a local operator $\mathcal{O}$ between single-particle bra and ket states, and we develop methods that significantly reduce errors resulting from the finite truncation of the Hilbert space. We extrapolate these form factors as a function of momentum to the regime where, by crossing symmetry, they are form factors of $\mathcal{O}$ between the vacuum and a two-particle asymptotic scattering state. We also compute the momentum-space time-ordered two-point functions of local operators in LCT. These converge quickly at momenta away from branch cuts, allowing us to indirectly obtain the time-ordered correlator and the spectral density at the branch cuts. We focus on the case where the local operator $\mathcal{O}$ is the trace Θ of the stress tensor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Bootstrapping 2d ϕ 4 theory with Hamiltonian truncation data

We combine the methods of Hamiltonian Truncation and the recently proposed generalisation of the S-matrix bootstrap that includes local operators to determine the two-particle scattering amplitude and the two-particle form factor of the stress tensor at s > 0 in the 2d Φ 4 theory. We use the form factor of the stress tensor at s ≤ 0 and its spectral density computed using Lightcone Conformal Truncation (LCT), and inject them into the generalized S-matrix bootstrap set-up. The obtained results for the scattering amplitude and the form factor are fully reliable only in the elastic regime. We independently construct the “pure” S-matrix bootstrap bounds (bootstrap without including matrix elements of local operators), and find that the sinh-Gordon model and its analytic continuation the “staircase model” saturate these bounds. Surprisingly, the Φ 4 two-particle scattering amplitude also very nearly saturates these bounds, and moreover is extremely close to that of the sinh-Gordon/staircase model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Harmonic analysis of 2d CFT partition functions

We apply the theory of harmonic analysis on the fundamental domain of SL(2, Z) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space H/SL(2, Z), and of target space moduli space O(c, c; Z)\O(c, c; R)/O(c)×O(c). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS 3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Solving the 2D SUSY Gross-Neveu-Yukawa model with conformal truncation

We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a $\mathbb{Z}$ 2 -symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling $\overline{g}$, and is expected to have a critical point at a tuned value ${\overline{g}}_{\ast }$ where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the $\mathbb{Z}$ 2 symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of $\overline{g}$ and see the gap close as the critical point is approached, and numerically read off the critical exponent ν in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C -function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs

Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge C T , we clarify the properties of stress tensor composite primary operators of minimal twist, [ T m ], using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling $\left\langle {\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^m\right]\right\rangle$, where ${\mathcal{O}}_L$ is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling $\left\langle TT{\mathcal{O}}_L\right\rangle$, the three-point coupling $\left\langle {\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^2\right]\right\rangle$ is modified at large C T if $\left\langle TT{\mathcal{O}}_L\right\rangle \sim \sqrt{C_T}$. This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to ${\mathcal{O}}_L $ can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin- ℓ ≥ 2 bulk field at tree level, or any spin ℓ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Nonperturbative matching between equal-time and lightcone quantization

We investigate the nonperturbative relation between lightcone (LC) and standard equal-time (ET) quantization in the context of λΦ4 theory in d = 2. We discuss the perturbative matching between bare parameters and the failure of its naive nonperturbative extension. We argue that they are nevertheless the same theory nonperturbatively, and that furthermore the nonperturbative map between bare parameters can be extracted from ET perturbation theory via Borel resummation of the mass gap. We test this map by using it to compare physical quantities computed using numerical Hamiltonian truncation methods in ET and LC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Probing universalities in d > 2 CFTs: from black holes to shockwaves

Gravitational shockwaves are insensitive to higher-curvature corrections in the action. Recent work found that the OPE coefficients of lowest-twist multi-stress-tensor operators, computed holographically in a planar black hole background, are insensitive as well. In this paper, we analyze the relation between these two limits. We explicitly evaluate the two-point function on a shockwave background to all orders in a large central charge expansion. In the geodesic limit, we find that the ANEC exponentiates in the multi-stress-tensor sector. To compare with the black hole limit, we obtain a recursion relation for the lowest-twist products of two stress tensors in a spherical black hole background, letting us efficiently compute their OPE coefficients and prove their insensitivity to higher curvature terms. After resumming the lowest-twist stress-tensors and analytically continuing their contributions to the Regge limit, we find a perfect agreement with the shockwave computation. We also discuss the role of double-trace operators, global degenerate states, and multi-stress-tensor conformal blocks. These holographic results suggest the existence of a larger universal structure in higher-dimensional CFTs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Universal lowest-twist in CFTs from holography

We probe the conformal block structure of a scalar four-point function in d ≥ 2 conformal field theories by including higher-order derivative terms in a bulk gravitational action. We consider a heavy-light four-point function as the boundary correlator at large central charge. Such a four-point function can be computed, on the gravity side, as a two-point function of the light operator in a black hole geometry created by the heavy operator. We consider analytically solving the corresponding scalar field equation in a near-boundary expansion and find that the multi-stress tensor conformal blocks are insensitive to the horizon boundary condition. The main result of this paper is that the lowest-twist operator product expansion (OPE) coefficients of the multi-stress tensor conformal blocks are universal: they are fixed by the dimension of the light operators and the ratio between the dimension of the heavy operator and the central charge CT. Neither supersymmetry nor unitary is assumed. Higher-twist coefficients, on the other hand, generally are not protected. A recursion relation allows us to efficiently compute universal lowest-twist coefficients. The universality result hints at the potential existence of a higher-dimensional Virasoro-like symmetry near the lightcone. While we largely focus on the planar black hole limit in this paper, we include some preliminary analysis of the spherical black hole case in an appendix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

The bulk-to-boundary propagator in black hole microstate backgrounds

First-quantized propagation in quantum gravitational AdS 3 backgrounds can be exactly reconstructed using CFT 2 data and Virasoro symmetry. We develop methods to compute the bulk-to-boundary propagator in a black hole microstate, ⟨ϕ L O L O H O H ⟩, at finite central charge. As a first application, we show that the semiclassical theory on the Euclidean BTZ solution sharply disagrees with the exact description, as expected based on the resolution of forbidden thermal singularities, though this effect may appear exponentially small for physical observers.

1/N expansion↗
DOE OSTI2019

The most irrational rational theories

We propose a two-parameter family of modular invariant partition functions of two-dimensional conformal field theories (CFTs) holographically dual to pure threedimensional gravity in anti de Sitter space. Our two parameters control the central charge, and the representation of SL(2, $\mathbb{Z}$). At large central charge, the partition function has a gap to the first nontrivial primary state of $\frac{c}{24}$. As the SL(2, $\mathbb{Z}$) representation dimension gets large, the partition function exhibits some of the qualitative features of an irrational CFT. This, for instance, is captured in the behavior of the spectral form factor. As part of these analyses, we find similar behavior in the minimal model spectral form factor as c approaches 1.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Conformal truncation of chern-simons theory at large $N$ f

We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons field coupled to N f fermions in the limit of large Nf using conformal truncation, i.e. with a truncated space of states corresponding to primary operators with dimension below a maximum cutoff Δ max . In both the Chern-Simons theory, and in the O(N) model at infinite N, we compute the current spectral functions analytically as a function of Δ max and reproduce previous results in the limit that the truncation Δ max is taken to ∞. Along the way, we determine how to preserve gauge invariance and how to choose an optimal discrete basis for the momenta of states in the truncation space.

1/N expansion, Chern-Simons Theories↗
DOE OSTI2018

Lightcone effective Hamiltonians and RG flows

We introduce a prescription for an effective lightcone (LC) Hamiltonian that includes the effects of zero modes, focusing on the case of Conformal Field Theories (CFTs) deformed by relevant operators. We display how the prescription resolves a number of issues with LC quantization, including i) the apparent non-renormalization of the vacuum, ii) discrepancies in critical values of bare parameters in equal-time vs LC quantization, and iii) an inconsistency at large N in CFTs with simple AdS duals. We describe how LC quantization can drastically simplify Hamiltonian truncation methods applied to some large N CFTs, and discuss how the prescription identifies theories where these simplifications occur. We demonstrate and check our prescription in a number of examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

The AdS 3 propagator and the fate of locality

We recently used Virasoro symmetry considerations to propose an exact formula for a bulk proto-field φ in AdS 3 . In this paper we study the propagator <φφ>. We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results from recursion are expanded at large central charge, they match gravitational perturbation theory for a free scalar field coupled to gravity in our chosen gauge. We find that although the propagator is finite and well-defined at long distances, its perturbative expansion in G N = 3 2 c exhibits UV/IR mixing effects. If we nevertheless interpret <φφ> as a probe of bulk locality, then when G N m &#x03D5;<!-- φ --> &#x226A;<!-- << --> 1 locality breaks down at the new short-distance scale &#x03C3;<!-- σ --> &#x2217;<!-- * --> &#x223C;<!-- ~ --> G N R A d S 3 4 . For φ with very large bulk mass, or at small central charge, bulk locality fails at the AdS length scale. In all cases, locality ‘breakdown’ manifests as singularities or branch cuts at spacelike separation arising from non-perturbative quantum gravitational effects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗