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S. Nagy

Publications and source records attributed to S. Nagy.

At least 19 recordsLinked to original sources
arXiv2025

Classical limit of a scalar quantum field theory

It is well known that a minimal distance emerges in quantum field theories owing to the need to regularize the UV divergences. The macroscopical limit at large minimal distance, weak spatial resolution, is investigated for a self interacting scalar quantum field theory by the help of the renormalization group. The lowering of the cutoff always opens the dynamics hence the renormalization group has to be implemented for open quantum field theories. A strongly coupled non-relativistic scaling regime is found supporting a second order phase transition between weakly and strongly open theories. The weakly (strongly) open bare theories develop into strongly (weakly) open dynamics during the renormalization group flow. The two known conditions of classical limit, the strong decoherence and the suppression of the quantum fluctuations are confirmed for closed bare theories at distances beyond a non-relativistic correlation length.

hep-th↗
arXiv2024

First order phase transition with functional renormalization group method

The renormalization group method, more specifically the Wegner-Houghton equation, is used to find first order phase transitions in a simple scalar field theory with a polynomial potential. An improved definition of the running parameters allows us to explore the renormalization group flow down to the IR end point and to locate phase transitions. Beyond the expected first order transition further radiative correction generated first and second order transitions are found. The phase diagram is reviewed by a Monte-Carlo simulation of the lattice regulated version of the theory but the serious slow down of the convergence prevents us to obtain conclusive results from the simulation.

hep-th↗
arXiv2022

Interpolation formulas for asymptotically safe cosmology

Simple interpolation formulas are proposed for the description of the renormalization group (RG) scale dependences of the gravitational couplings in the framework of the 2-parameters Einstein-Hilbert (EH) theory of gravity and applied to a simple, analytically solvable, spatially homogeneous and isotropic, spatially flat model universe. The analytical solution is found in two schemes incorporating different methods of the determination of the conversion rule $k(t)$ of the RG scale $k$ to the cosmological time $t$. In the case of the discussed model these schemes turn out to yield identical cosmological evolution. Explicit analytical formulas are found for the conversion rule $k(t)$ as well as for the characteristic time scales $t_G$ and $t_\Lambda>t_G$ corresponding to the dynamical energy scales $k_G$ and $k_\Lambda$, respectively, arising form the RG analysis of the EH theory. It is shown that there exists a model-dependent time scale $t_d$ ($t_G\le t_d<t_\Lambda$) at which the accelerating expansion changes to the decelerating one. It is shown that the evolution runs from a well-identified cosmological fixed point to another one. As a by-product we show that the entropy of the system decreases monotonically in the interval $0<t\le t_\Lambda$ due to the quantum effects.

gr-qc↗
arXiv2022

On the Lorentz symmetry in conformally reduced Quantum Gravity

The functional renormalization group treatment of the conform reduced Einstein-Hilbert gravity is extended by following the evolution of the time and space derivatives separately, in order to consider the Lorentz symmetry during the evolution. We found the Reuter fixed point in the ultraviolet region. It is shown that starting from the Gaussian fixed point the Lorentz symmetry breaks down in the vicinity of the Reuter fixed point. Similarly, in the symmetry broken phase it also breaks down in the infrared region close to a critical singularity scale. By calculating the anomalous dimension form the kinetic term of the action, we found a new relevant coupling belonging to the curvature.

hep-th↗
arXiv2021

Odd dimensional analogue of the Euler characteristic

When compact manifolds $X$ and $Y$ are both even dimensional, their Euler characteristics obey the K\"unneth formula $\chi(X\times Y)=\chi(X) \chi(Y)$. In terms of the Betti numbers $b_p(X)$, $\chi(X)=\sum_{p}(-1)^p b_p(X)$, implying that $\chi(X)=0$ when $X$ is odd dimensional. We seek a linear combination of Betti numbers, called $\rho$, that obeys an analogous formula $\rho(X\times Y)=\chi(X) \rho(Y)$ when $Y$ is odd dimensional. The unique solution is $\rho(Y)=-\sum_{p}(-1)^p p b_p(Y)$. Physical applications include: (1) $\rho \rightarrow (-1)^m \rho $ under a generalized mirror map in $d=2m+1$ dimensions, in analogy with $\chi \rightarrow (-1)^m \chi $ in $d=2m$; (2) $\rho$ appears naturally in compactifications of M-theory. For example, the 4-dimensional Weyl anomaly for M-theory on $X^4 \times Y^7$ is given by $\chi(X^4)\rho(Y^7)=\rho(X^4 \times Y^7) $ and hence vanishes when $Y^7$ is self-mirror. Since, in particular, $\rho(Y\times S^1)=\chi(Y)$, this is consistent with the corresponding anomaly for Type IIA on $X^4 \times Y^6$, given by $\chi(X^4)\chi(Y^6)=\chi(X^4 \times Y^6)$, which vanishes when $Y^6$ is self-mirror; (3) In the partition function of $p$-form gauge fields, $\rho$ appears in odd dimensions as $\chi$ does in even.

hep-th↗
arXiv2021

Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions

A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of `gravity $=$ gauge $\times$ gauge'. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the `gauge $\times$ gauge' convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

hep-th↗
arXiv2020

Renormalizing open quantum field theories

The functional renormalization group flow of a scalar field theory with quartic couplings and a sharp spatial momentum cutoff is presented in four-dimensional Minkowski space-time for the bare action by retaining the entanglement of the IR and the UV particle modes. It is argued that the open interaction channels have to be taken into account in quantum field theory defined by the help of a cutoff, and a non-perturbative UV-IR entanglement is found in closed or almost closed models.

hep-th↗
arXiv2019

Gauge $\times$ Gauge on Spheres

We introduce a convolution on a 2-sphere and use it to show that the linearised Becchi-Rouet-Stora-Tyutin transformations and gauge fixing conditions of Einstein-Hilbert gravity coupled to a two-form and a scalar field, follow from the product of two Yang-Mills theories. This provides an example of the convolutive product of gauge theories on a non-trivial background. By introducing a time direction the product is shown to extend to the $D=1+2$ Einstein-static universe.

hep-th↗
arXiv2019

Renormalization in Minkowski space-time

The multiplicative and the functional renormalization group methods are applied for the four dimensional scalar theory in Minkowski space-time. It is argued that the appropriate choice of the subtraction point is more important in Minkowski than in Euclidean space-time. The parameters of the cutoff theory, defined by a subtraction point in the quasi-particle domain, are complex due to the mass-shell contributions and the renormalization group flow becomes much more involved than its Euclidean counterpart.

hep-th↗
arXiv2018

Renormalization of the bilocal sine-Gordon model

The functional renormalization group treatment is presented for the two-dimensional sine-Gordon model by including a bilocal term in the potential, which contributes to the flow at tree level. It is shown that the flow of the bilocal term can substitute the evolution of the wave function renormalization constant, and then the Kosterlitz-Thouless type phase transition can be recovered.

hep-th↗
arXiv2018

Gravity as Gauge Theory Squared: A Ghost Story

The Becchi-Rouet-Stora-Tyutin (BRST) transformations and equations of motion of a gravity-two-form-dilaton system are derived from the product of two Yang-Mills theories in a BRST covariant form, to linear approximation. The inclusion of ghost fields facilitates the separation of the graviton and dilaton. The gravitational gauge fixing term is uniquely determined by those of the Yang-Mills factors which can be freely chosen. Moreover, the resulting gravity-two-form-dilaton Lagrangian is anti-BRST invariant and the BRST and anti-BRST charges anti commute as a direct consequence of the formalism.

hep-th↗
arXiv2018

Modified renormalization group method applied to the $O(1)$ ghost model with periodic condensate

In order to discuss the occurrence of a periodic condensate in the Euclidean 3-dimensional ghost $O(1)$ model, a modified version of the effective average action (EAA) renormalization group (RG) method is developed, called by us Fourier-Wetterich RG approach. It is proposed to start with an ansatz for the EAA, that contains terms, in addition to the usual ones, induced by the various Fourier-modes of the periodic condensate and to expand the EAA in functional Taylor-series around the periodic background. The RG flow equations are derived in the next-to-next-to-leading order of the gradient expansion (GE). No field-dependence of the derivative couplings have been taken into account and $Z_2$ symmetry of the EAA is preserved. Preliminary numerical results have been obtained under various additional simplifying assumptions. The characteristics of the Wilson-Fisher fixed point and the phase structure of the model have been determined numerically in the local potential approximation and in the next-to-leading order of the GE, when the periodic condensate has been modelled by a single cosine mode in one spatial direction. From the preliminary results important information is gained on further possibilities to improve the proposed RG scheme.

hep-th↗
arXiv2018

Euclidean scalar field theory in the bi-local approximation

The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bi-local saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean $\phi^6$ model in this work. The phase structure is changed, new phases and relevant operators are found and certain universality classes are restricted by the bi-local saddle point.

hep-th↗
arXiv2017

The Magic Star of Exceptional Periodicity

We present a periodic infinite chain of finite generalisations of the exceptional structures, including e8, the exceptional Jordan algebra (and pair), and the octonions. We demonstrate that the exceptional Jordan algebra is part of an infinite family of finite-dimensional matrix algebras (corresponding to a particular class of cubic Vinberg's T-algebras). Correspondingly, we prove that e8 is part of an infinite family of algebras (dubbed "Magic Star" algebras) that resemble lattice vertex algebras.

hep-th↗
arXiv2017

Regulator dependence of fixed points in quantum Einstein gravity with $R^2$ truncation

We performed a functional renormalization group analysis for the quantum Einstein gravity including a quadratic term in the curvature. The ultraviolet non-gaussian fixed point and its critical exponent for the correlation length are identified for different forms of regulators in case of dimension 3. We searched for that optimized regulator where the physical quantities show the least regulator parameter dependence. It is shown that the Litim regulator satisfies this condition. The infrared fixed point has also been investigated, it is found that the exponent is insensitive to the third coupling introduced by the $R^2$ term.

hep-th↗
arXiv2017

Are all supergravity theories Yang-Mills squared?

Using simple symmetry arguments we classify the ungauged $D=4$, $\mathcal{N}=2$ supergravity theories, coupled to both vector and hyper multiplets through homogeneous scalar manifolds, that can be built as the product of $\mathcal{N}=2$ and $\mathcal{N}=0$ matter-coupled Yang-Mills gauge theories. This includes all such supergravities with two isolated exceptions: pure supergravity and the $T^3$ model.

hep-th↗
arXiv2017

Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models

The effect of the $\ord{\partial^4}$ terms of the gradient expansion on anomalous dimension $\eta$ and the correlation length's critical exponent $\nu$ of the Wilson-Fisher fixed point has been determined for the Euclidean $O(N)$ model for $N=1$ and the number of dimensions $2< d<4$ as well as for $N\ge 2$ and $d=3$. Wetterich's effective average action renormalization group method is used with field-independent derivative couplings and Litim's optimized regulator. It is shown that the critical theory for $N\ge 2$ is well approximated by the effective average action preserving $O(N)$ symmetry with the accuracy of $\ord{\eta}$.

hep-th↗