Snowmass Theory Frontier Report
This report summarizes the recent progress and promising future directions in theoretical high-energy physics (HEP) identified within the Theory Frontier of the 2021 Snowmass Process.
hep-ph↗
arXiv subjects
S. Catterall
Publications and source records attributed to S. Catterall.
Report of the Snowmass 2013 Computing Frontier working group on Lattice Field Theory -- Lattice field theory for the energy and intensity frontiers: Scientific goals and computing needs
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
hep-lat↗
Stripes from (noncommutative) stars
We show that lattice regularization of noncommutative field theories can be used to study non-perturbative vacuum phases. Specifically we provide evidence for the existence of a striped phase in two-dimensional noncommutative scalar field theory
hep-lat↗
Testing a Fourier Accelerated Hybrid Monte Carlo Algorithm
We describe a Fourier Accelerated Hybrid Monte Carlo algorithm suitable for dynamical fermion simulations of non-gauge models. We test the algorithm in supersymmetric quantum mechanics viewed as a one-dimensional Euclidean lattice field theory. We find dramatic reductions in the autocorrelation time of the algorithm in comparison to standard HMC.
hep-lat↗
A Two-Dimensional Lattice Model with Exact Supersymmetry
Starting from a simple discrete model which exhibits a supersymmetric invariance we construct a local, interacting, two-dimensional Euclidean lattice theory which also admits an exact supersymmetry. This model is shown to correspond to the Wess-Zumino model with extended N=2 supersymmetry in the continuum. We have performed dynamical fermion simulations to check the spectrum and supersymmetric Ward identities and find good agreement with theory.
hep-lat↗
Reconstructing the conformal mode in simplicial gravity
We verify that summing 2D DT geometries correctly reproduces the Polyakov action for the conformal mode, including all ghost contributions, at large volumes. The Gaussian action is reproduced even for central charges greater than one lending strong support to the hypothesis that the space of all possible dyamical triangulations approximates well the space of physically distinct metrics independent of the precise nature of the matter coupling.
hep-lat↗
The Conformal Mode in 2D Simplicial Gravity
We verify that summing 2D DT geometries correctly reproduces the Polyakov action for the conformal mode, including all ghost contributions, at large volumes. The Gaussian action is reproduced even for c=10, well into the branched polymer phase, which confirms the expectation that the DT measure is indeed correct in this regime as well.
hep-lat↗
Dynamics of the Conformal Mode and Simplicial Gravity
We review the derivation of the Liouville action in 2DQG via the trace anomaly and emphasize how a similar approach can be used to derive an effective action describing the long wavelength dynamics of the conformal factor in 4D. In 2D we describe how to make an explicit connection between dynamical triangulations and this continuum theory, and present results which confirm the equivalance of the two approaches. By reconstructing a lattice conformal mode from DT simulations it should be possible to test this equivalence in 4D also.
hep-lat↗
Anisotropic Membranes
We describe the statistical behavior of anisotropic crystalline membranes. In particular we give the phase diagram and critical exponents for phantom membranes and discuss the generalization to self-avoiding membranes.
hep-lat↗
Singular Structure in 4D Simplicial Gravity
We show that the phase transition previously observed in dynamical triangulation models of quantum gravity can be understood as being due to the creation of a singular link. The transition between singular and non-singular geometries as the gravitational coupling is varied appears to be first order.
hep-lat↗
The flat phase of fixed-connectivity membranes
The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical understanding of the remarkable flat phase of such membranes. We then summarize the results of a recent large scale Monte Carlo simulation of the simplest conceivable discrete realization of this system \cite{BCFTA}. We verify the existence of long-range order, determine the associated critical exponents of the flat phase and compare the results to the predictions of various theoretical models.
hep-lat↗
Simplicial Gravity in Dimension Greater than Two
We consider two issues in the DT model of quantum gravity. First, it is shown that the triangulation space for D>3 is dominated by triangulations containing a single singular (D-3)-simplex composed of vertices with divergent dual volumes. Second we study the ergodicity of current simulation algorithms. Results from runs conducted close to the phase transition of the four-dimensional theory are shown. We see no strong indications of ergodicity br eaking in the simulation and our data support recent claims that the transition is most probably first order. Furthermore, we show that the critical properties of the system are determined by the dynamics of remnant singular vertices.
hep-lat↗
The Flat Phase of Crystalline Membranes
We present the results of a high-statistics Monte Carlo simulation of a phantom crystalline (fixed-connectivity) membrane with free boundary. We verify the existence of a flat phase by examining lattices of size up to $128^2$. The Hamiltonian of the model is the sum of a simple spring pair potential, with no hard-core repulsion, and bending energy. The only free parameter is the the bending rigidity $κ$. In-plane elastic constants are not explicitly introduced. We obtain the remarkable result that this simple model dynamically generates the elastic constants required to stabilise the flat phase. We present measurements of the size (Flory) exponent $ν$ and the roughness exponent $ζ$. We also determine the critical exponents $η$ and $η_u$ describing the scale dependence of the bending rigidity ($κ(q) \sim q^{-η}$) and the induced elastic constants ($λ(q) \sim μ(q) \sim q^{η_u}$). At bending rigidity $κ= 1.1$, we find $ν= 0.95(5)$ (Hausdorff dimension $d_H = 2/ν= 2.1(1)$), $ζ= 0.64(2)$ and $η_u = 0.50(1)$. These results are consistent with the scaling relation $ζ= (2+η_u)/4$. The additional scaling relation $η= 2(1-ζ)$ implies $η= 0.72(4)$. A direct measurement of $η$ from the power-law decay of the normal-normal correlation function yields $η\approx 0.6$ on the $128^2$ lattice.
cond-mat↗
Singular Vertices and the Triangulation Space of the D-sphere
By a sequence of numerical experiments we demonstrate that generic triangulations of the $D-$sphere for $D>3$ contain one {\it singular} $(D-3)-$simplex. The mean number of elementary $D-$simplices sharing this simplex increases with the volume of the triangulation according to a simple power law. The lower dimension subsimplices associated with this $(D-3)-$simplex also show a singular behaviour. Possible consequences for the DT model of four-dimensional quantum gravity are discussed.
hep-lat↗
Lattice Quantum Gravity: Review and Recent Developments
We review the status of different approaches to lattice quantum gravity indicating the successes and problems of each. Recent developments within the dynamical triangulation formulation are then described. Plenary talk at LATTICE 95 July 11-15, Melbourne, Australia.
hep-lat↗
A Real-Space Renormalization Group for Random Surfaces
We propose a new real-space renormalization group transformation for dynamical triangulations. It is shown to preserve geometrical exponents such as the string susceptibility and Hausdorff dimension. We furthermore show evidence for a fixed point structure both in pure gravity and gravity coupled to a critical Ising system. In the latter case we are able to extract estimates for the gravitationally dressed exponents which agree to within 2-3% of the KPZ formula.
hep-lat↗
Scaling and the Fractal Geometry of Two-Dimensional Quantum Gravity
We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure gravity we find d_H approx. 3.8, in support of recent theoretical calculations that d_H = 4. We also discuss the back-reaction of matter on the geometry.
hep-lat↗
Entropy and the Approach to the Thermodynamic Limit in Three-Dimensional Simplicial Gravity
We present numerical results supporting the existence of an exponential bound in the dynamical triangulation model of three-dimensional quantum gravity.Both the critical coupling and various other quantities show a slow power law approach to the infinite volume limit.
hep-lat↗