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Daniel Friedan

Publications and source records attributed to Daniel Friedan.

At least 19 recordsLinked to original sources
arXiv2023

Global structure of euclidean quantum gravity

Euclidean quantum gravity (EQG) separates into a local theory and a global theory. The local theory operates in every compact $d$-manifold with boundary to produce a state on the boundary. The global theory then sums these boundary states over the diffeomorphism classes of $d$-manifolds with boundary to make the Hartle-Hawking state. Global EQG is formulated here as classical statistical physics. The Hartle-Hawking state is the probability measure of a mathematically natural classical statistical system, analogous to the functional measure of euclidean quantum field theory. General principles of global EQG determine the numerical weights $w(M)$ in the sum over diffeomorphism classes $M$.

hep-th↗
arXiv2022

The CGF dark matter fluid

The cosmological gauge field (CGF) is a classical solution of SU(2)-weak gauge theory oscillating rapidly in time. It is the dark matter driving the CGF cosmology. A general, local, mathematically natural construction of the CGF is given here. The macroscopic properties are derived. The CGF is an irrotational perfect fluid. It provides a synchronized global time coordinate and a global rest frame. There is a conserved number density. The energy density and pressure are related by the same equation of state as derived in the CGF cosmology and used in the TOV stellar structure equations for stars made of CGF dark matter. The present construction justifies the TOV solution. Some possible routes towards testing the theory are suggested at the end.

physics.gen-ph↗
arXiv2022

First principles cosmology of the Standard Model epoch

This is a short summary of a project to construct a first principles cosmology of the Standard Model epoch, the period starting shortly before the electro-weak transition. The cosmology is derived from a simple initial state entirely within the SM and General Relativity. The initial state is semi-classical -- concentrated near a classical solution of the SM equations of motion -- and is precisely specified by a few simple conditions. The dark matter is a classical effect, a coherent state of the SU(2)-weak gauge field and the Higgs field. The leading order, classical universe contains only the dark matter. Ordinary matter is a correction due to the fluctuations of the SM fields around the classical trajectory. The initial state produces a homogeneous, isotropic, flat universe. There are no adjustable parameters. No physics beyond the SM is invoked. Only the classical calculations have been done so far. The time evolution of the fluctuations remains to be calculated.

astro-ph.CO↗
arXiv2022

Dark matter stars

The dark matter in the CGF cosmology is a cosmological SU(2)-weak gauge field (the CGF). The TOV stellar structure equations are solved numerically for stars composed of this dark matter. The star mass M can take any value up to a maximum $9.14 \times 10^{-6}$ M_sun. For each value of M the star radius R lies between 5.23cm and 13.6cm. More than one value of R is possible when M > $5.09 \times 10^{-6}$ M_sun. For those stars, a transition from larger to smaller R would release gravitational energy on the order of $10^{41}$J in a time on the order of $10^{-10}$s.

astro-ph.CO↗
arXiv2022

A theory of the dark matter

In an earlier paper I proposed a highly symmetric semi-classical initial condition to describe the universe in the period leading up to the electroweak transition and completely determine all cosmology after that. Nothing beyond the Standard Model is assumed. Inflation is not needed. The initial symmetry allows no adjustable parameters. It is a complete theory of the Standard Model cosmological epoch, predictive and falsifiable. Here, the time evolution of the initial condition is calculated in the classical approximation. The fields with nontrivial classical values are the SU(2)-weak gauge field (the cosmological gauge field or CGF) and the Higgs field. The CGF produces the electroweak transition then evolves as a non-relativistic perfect fluid ($w_{\mathrm{CGF}}\approx 0$). At the present time, i.e. when $H=H_{0}$, the CGF energy density satisfies $\Omega_{\Lambda}+\Omega_{\mathrm{CGF}}=1$. The CGF is the dark matter. The dark matter is a classical phenomenon of the Standard Model. The classsical universe contains only the dark matter, no ordinary matter. At next to leading order the fluctuations of the Standard Model fields will provide a calculable, relatively small amount of ordinary matter such that $\Omega_{\Lambda}+\Omega_{\mathrm{CGF}}+\Omega_{\mathrm{ordinary}}=1$.

astro-ph.CO↗
arXiv2022

Thermodynamic stability of a cosmological SU(2)-weak gauge field

The CGF cosmology is a complete theory of cosmology from the electroweak transition onward. It is semi-classical. At leading order the only matter is dark matter -- a cosmological SU(2)-weak gauge field (the CGF). Ordinary matter is a subleading correction from fluctuations around the classical state. The CGF is periodic in imaginary time. It acts as thermal bath for the fluctuations of the Standard Model fields. Here, the initial thermal state of the SU(2) gauge field fluctuations is constructed and shown to be thermodynamically stable. This is a warm-up for (1) constructing the initial thermal state of all the fluctuations in order to calculate its time evolution and (2) showing that initial state to be thermodynamically stable in order to show that the CGF cosmology is physically natural.

hep-th↗
arXiv2020

Cosmology from the two-dimensional renormalization group acting as the Ricci flow

The two-dimensional renormalization group acting as the Ricci flow $Λ\frac{\partial}{\partialΛ} g_{μν} = R_{μν}$ produces a specific 1+3 dimensional space-time metric which describes an expanding universe that starts with a big bang $a \sim t^{\scriptscriptstyle 1/\sqrt3}$ then decelerates until $z=0.2$ then accelerates until ending at $t_{\max}=1.6\,t_{H}$ with a big blowup $a \sim (t_{\max}-t)^{\scriptscriptstyle -1/\sqrt3}$. The only free parameters are the overall time scale and the value of the present time $t_{0}$. These are fixed by the Hubble constant $H_{0}=t_{H}^{-1}$ and the present deceleration parameter $q(t_{0})$. This crude calculation of cosmology omits all but the gravitational field. The only energy-momentum is purely gravitational dark matter and energy. This is a preliminary exploration towards a specific, comprehensive, testable calculation of cosmology from a fundamental theory in which physics is produced by a quantum version of the two-dimensional renormalization group.

astro-ph.CO↗
arXiv2020

Origin of cosmological temperature

A classical solution of the Standard Model + General Relativity is given by an elliptic function whose periodicity in imaginary time is the origin of cosmological temperature. Nothing beyond the Standard Model is assumed. The solution is a $\mathrm{Spin}(4)$-symmetric universe expanding prior to the electroweak transition. A rapidly oscillating $\mathrm{SU}(2)$ gauge field holds the Higgs field to $0$ with strength inversely proportional to the scale factor $a$. When $a$ reaches $a_{\scriptscriptstyle\mathrm{EW}}$ the solution becomes unstable and the electoweak transition begins. $a_{\scriptscriptstyle\mathrm{EW}}$ is the only free parameter in the solution. The temperature at $a_{\scriptscriptstyle\mathrm{EW}}$ is $m_{H}/{(6π)^{1/2}} = 28.8\,\text{GeV} = 3.34 \times 10^{14}\, \text{K}$ whatever the value of $a_{\scriptscriptstyle\mathrm{EW}}$.

astro-ph.CO↗
arXiv2019

Entropy flow in near-critical quantum circuits

Near-critical quantum circuits are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective excitations evolve reversibly, effectively isolated from the environment. The design of reversible computers is constrained by the laws governing entropy flow within the computer. In near-critical quantum circuits, entropy flows as a locally conserved quantum current, obeying circuit laws analogous to the electric circuit laws. The quantum entropy current is just the energy current divided by the temperature. A quantum circuit made from a near-critical system (of conventional type) is described by a relativistic 1+1 dimensional relativistic quantum field theory on the circuit. The universal properties of the energy-momentum tensor constrain the entropy flow characteristics of the circuit components: the entropic conductivity of the quantum wires and the entropic admittance of the quantum circuit junctions. For example, near-critical quantum wires are always resistanceless inductors for entropy. A universal formula is derived for the entropic conductivity: σ_S(ω)=iv^{2}S/ωT, where ωis the frequency, T the temperature, S the equilibrium entropy density and v the velocity of `light'. The thermal conductivity is Real(Tσ_S(ω))=πv^{2}Sδ(ω). The thermal Drude weight is, universally, v^{2}S. This gives a way to measure the entropy density directly.

cond-mat.stat-mech↗
arXiv2019

Entropy flow through near-critical quantum junctions

This is the continuation of cond-mat/0505084. Elementary formulas are derived for the flow of entropy through a circuit junction in a near-critical quantum circuit, based on the structure of the energy-momentum tensor at the junction. The entropic admittance of a near-critical junction in a bulk-critical circuit is expressed in terms of commutators of the chiral entropy currents. The entropic admittance at low frequency, divided by the frequency, gives the change of the junction entropy with temperature -- the entropic `capacitance'. As an example, and as a check on the formalism, the entropic admittance is calculated explicitly for junctions in bulk-critical quantum Ising circuits (free fermions, massless in the bulk), in terms of the reflection matrix of the junction. The half-bit of information capacity per end of critical Ising wire is re-derived by integrating the entropic `capacitance' with respect to temperature, from T=0 to T=infinity.

cond-mat.stat-mech↗
arXiv2018

A pragmatic approach to formal fundamental physics

A minimal practical formal structure for a fundamental theory is suggested. A mechanism that produces such a structure is reviewed. The proposed mechanism has possibilities of producing non-canonical phenomena in SU(2) and SU(3) quantum gauge theories. These might provide testable conditional predictions. One possibility is a vacuum condensate of SU(2) gauge fields associated to certain trajectories of the SU(2) Yang-Mills flow. Contents 1 Formal fundamental physics 1.1 Against Quantum Gravity 1.2 Against mathematical idealizations 2 A minimal practical formal structure 2.1 An effective QFT for distances > L and an effective S-matrix for distances < L, for observers at every scale L >> l_P 2.2 QFT renormalization group operates from smaller distance L to larger; S-matrix renormalization group operates from larger L to smaller 2.3 An S-matrix does not imply a hamiltonian 3 A mechanism that produces such a formal structure 3.1 Summary 3.2 2d-QFT of the string worldsheet 3.3 Effective string S-matrix with IR cutoff L 3.4 Effective 2d coupling constants 3.5 Implement the S-matrix renormalization group 3.6 Production of an effective QFT with UV cutoff L 3.7 Possible non-canonical degrees of freedom and couplings in SU(2) and SU(3) quantum gauge theory 3.8 2d winding modes and 2d instantons 3.9 Vacuum condensate of SU(2) Yang-Mills flow defects 4 To do Appendix. Notes on the line of thought A.1 Search for a mechanism that produces QFT A.2 Pragmatism and the S-matrix philosophy

hep-th↗
arXiv2017

A new kind of quantum field theory of (n-1)-dimensional defects in 2n dimensions

I describe a project to open a new territory of quantum field theory where the fields live not on a space-time manifold but on certain complete metric spaces of (n-1)-dimensional objects (defects) in a 2n-dimensional space-time M. These metric spaces are "quasi Riemann surfaces"; they are formally analogous to Riemann surfaces. Every construction of a 2d conformal field theory is to give an analogous construction of a cft on the quasi Riemann surfaces, and thereby a cft on M. The global symmetry group of the 2d cft becomes a local gauge symmetry. Ordinary local quantum fields in space-time are constructed by restricting to small objects. The project is based on writing the free n-form in 2n dimensions as the 2d gaussian model on the quasi Riemann surfaces. This note is a summary of the main points of arXiv:1605.03279.

hep-th↗
arXiv2016

Quantum field theories of extended objects

First steps are taken in a project to construct a general class of conformal and perhaps, eventually, non-conformal quantum field theories of (n-1)-dimensional extended objects in a d=2n dimensional conformal space-time manifold M. The fields live on the spaces E of relative integral (n-1)-cycles in M -- the integral (n-1)-currents of given boundary. Each E is a complete metric space geometrically analogous to a Riemann surface $Σ$. For example, if $M=S^d$, $Σ= S^2$. The quantum fields on E are to be mapped to observables in a 2d CFT on $Σ$. The correlation functions on E are to be given by the 2d correlation functions on $Σ$. The goal is to construct a CFT of extended objects in d=2n dimensions for every 2d CFT, and eventually a non-conformal QFT of extended objects for every non-conformal 2d QFT, so that all the technology of 2d QFT can be applied to the construction and analysis of quantum field theories of extended objects. The project depends crucially on settling some mathematical questions about analysis in the spaces E. The project also depends on extending the observables of 2d CFT from the finite sets of points in a Riemann surface to the integral 0-currents.

hep-th↗
arXiv2015

Cauchy conformal fields in dimensions d>2

Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined everywhere once we know their value on a codimension 1 surface. We classify all the unitary Cauchy fields. By analyzing the mode expansion on the unit sphere, we show that all unitary Cauchy fields are free in the sense that their correlation functions factorize on the 2-point function. We also discuss the possibility of non-unitary Cauchy fields and classify them in d=3 and 4.

hep-th↗
arXiv2013

Constraints on 2d CFT partition functions

Modular invariance is known to constrain the spectrum of 2d conformal field theories. We investigate this constraint systematically, using the linear functional method to put new improved upper bounds on the lowest gap in the spectrum. We also consider generalized partition functions of N = (2,2) superconformal theories and discuss the application of our results to Calabi-Yau compactifications. For Calabi-Yau threefolds with no enhanced symmetry we find that there must always be non-BPS primary states of weight 0.6 or less.

hep-th↗
arXiv2013

Precise lower bound on Monster brane boundary entropy

In this paper we develop further the linear functional method of deriving lower bounds on the boundary entropy of conformal boundary conditions in 1+1 dimensional conformal field theories (CFTs). We show here how to use detailed knowledge of the bulk CFT spectrum. Applying the method to the Monster CFT with c=\bar c=24 we derive a lower bound s > - 3.02 x 10^{-19} on the boundary entropy s=ln g, and find compelling evidence that the optimal bound is s>= 0. We show that all g=1 branes must have the same low-lying boundary spectrum, which matches the spectrum of the known g=1 branes, suggesting that the known examples comprise all possible g=1 branes, and also suggesting that the bound s>= 0 holds not just for critical boundary conditions but for all boundary conditions in the Monster CFT. The same analysis applied to a second bulk CFT -- a certain c=2 Gaussian model -- yields a less strict bound, suggesting that the precise linear functional bound on s for the Monster CFT is exceptional.

hep-th↗