arXiv subjects

Borut Bajc

Publications and source records attributed to Borut Bajc.

At least 19 recordsLinked to original sources

arXiv2026

Infinite Heat Order in 3+1 Dimensions

We investigate whether spontaneous symmetry breaking can persist up to arbitrarily high temperature in ultraviolet-complete quantum field theories in four spacetime dimensions. We focus on completely asymptotically free models with gauge group $\mathrm{SU}(N_{c1})\times \mathrm{SU}(N_{c2})$ and two complex scalar fields, each transforming in the fundamental representation of one gauge factor and singlet under the other. The scalar potential contains quartic self-interactions together with a negative portal coupling between the two sectors. In the Veneziano limit, this class of theories was previously shown to admit fixed-flow trajectories for which one scalar acquires a negative thermal mass at asymptotically large temperature, leading to symmetry non-restoration. Here we extend that analysis to finite numbers of colours and flavours. We derive the finite-$N$ fixed-flow equations, compute the leading $1/N$ corrections to the large-$N$ solutions, and solve the full finite-$N$ system numerically. We find explicit finite-$N$ benchmark theories for which the scalar potential remains bounded from below, the gauge sector is asymptotically free, and one scalar thermal mass stays negative at arbitrarily high temperature. This provides an explicit perturbative example of infinite heat order in a four-dimensional ultraviolet-complete quantum field theory with a finite field content.

hep-th↗

arXiv2025

Holographic thermal propagator from modularity

It is known that the holographic thermal propagator in 4 spacetime dimensions can be related to the Nekrasov-Shatashvili limit of the $\Omega$-deformed ${\cal N}=2$ supersymmetric $SU(2)$ Yang-Mills theory with $N_f=4$ hypermultiplets. There are two expansions involved: one is the expansion in small temperature which in the Seiberg-Witten language is equivalent to the semiclassical expansion in inverse powers of the large adjoint vev and the second is the expansion in instanton numbers. Working in the simplified case of zero energy, we find that the latter expansion gives rise to quasi-modular forms which can be resummed as functions of Eisenstein series. The so obtained series in positive powers of small temperature shows clear signs of being asymptotic.

hep-th↗

arXiv2024

A realistic theory of $\mathrm{E_{6}}$ unification through novel intermediate symmetries

We propose a non-supersymmetric $\mathrm{E}_{6}$ GUT with the scalar sector consisting of $\mathbf{650}\oplus \mathbf{351'} \oplus \mathbf{27}$. Making use of the first representation for the initial symmetry breaking to an intermediate stage, and the latter two representations for second-stage breaking to the Standard Model and a realistic Yukawa sector, this theory represents the minimal $\mathrm{E}_{6}$ GUT that proceeds through one of the intermediate stages that are novel compared to $\mathrm{SU(5)}$ or $\mathrm{SO}(10)$ GUT: trinification $\mathrm{SU}(3)_C\times \mathrm{SU}(3)_L\times \mathrm{SU}(3)_R$, $\mathrm{SU}(6)\times \mathrm{SU}(2)$ and flipped $\mathrm{SO}(10)\times\mathrm{U}(1)$. We analyze these possibilities under the choice of vacuum that preserves a $\mathbb{Z}_{2}$ ``spinorial parity'', which disentangles the chiral and vector-like fermions of $\mathrm{E}_{6}$ and provides a dark matter candidate in the form of a (scalar) inert doublet. Three cases are shown to consistently unify under the extended survival hypothesis (with minimal fine-tuning): trinification symmetry $\mathrm{SU}(3)_C\times \mathrm{SU}(3)_L\times \mathrm{SU}(3)_R$ with either $LR$ or $CR$ parity, and $\mathrm{SU}(6)_{CR}\times\mathrm{SU}(2)_L$. Although the successful cases give a large range for proton lifetime estimates, all of them include regions consistent with current experimental bounds and within reach of forthcoming experiments. The scenario investigated in this paper essentially represents the unique (potentially) viable choice in the class of $\mathrm{E}_{6}$ GUTs proceeding through a novel-symmetry intermediate stage, since non-minimal alternatives seem to be intrinsically non-perturbative.

hep-ph↗

arXiv2023

UV finite GUT with SUSY Breaking

We provide an example of an ultraviolet finite supersymmetric grand unified theory of safe rather than free nature endowed with a supersymmetric dynamical breaking mechanism. Our results simultaneously enlarge the number of ultraviolet consistent supersymmetric grand unified theories while providing a relevant example of how to achieve a consistent ultraviolet safe extension of the Standard Model enjoying the benefits of grand unified theories.

hep-ph↗

arXiv2023

Trinification from $\mathrm{E}_{6}$ symmetry breaking

In the context of $\mathrm{E}_{6}$ Grand Unified Theories (GUTs), an intriguing possibility for symmetry breaking to the Standard Model (SM) group involves an intermediate stage characterized by either $\mathrm{SU}(3)\times\mathrm{SU}(3)\times\mathrm{SU}(3)$ (trinification) or $\mathrm{SU}(6)\times\mathrm{SU}(2)$. The more common choices of $\mathrm{SU(5)}$ and $\mathrm{SO}(10)$ GUT symmetry groups do not offer such breaking chains. We argue that the presence of a real (rank $2$ tensor) representation $\mathbf{650}$ of $\mathrm{E}_{6}$ in the scalar sector is the minimal and likely only reasonable possibility to obtain one of the novel intermediate stages. We analyze the renormalizable scalar potential of a single copy of the $\mathbf{650}$ and find vacuum solutions that support regularly embedded subgroups $\mathrm{SU}(3)\times\mathrm{SU}(3)\times\mathrm{SU}(3)$, $\mathrm{SU}(6)\times\mathrm{SU}(2)$, and $\mathrm{SO}(10)\times\mathrm{U}(1)$, as well as specially embedded subgroups $\mathrm{F}_{4}$ and $\mathrm{SU}(3)\times\mathrm{G}_{2}$ that do not contain the SM gauge symmetry. We show that for a suitable choice of parameters, each of the regular cases can be obtained as the lowest among the analyzed minima in the potential.

hep-ph↗

arXiv2023

Holographic thermal propagator for arbitrary scale dimensions

Using the AdS/CFT correspondence we model the behaviour of the two point correlator of an operator with arbitrary scale dimension $Δ$ in arbitrary spacetime dimension $d$ for small but non-zero temperature. The obtained propagator coincides in the low temperature regime with the known result for $d=4$ for large $Δ$ at the order $T^d$ as well as with the $T^d$ and $T^{2d}$ terms of the exact all order result for $d=2$. Furthermore, for arbitrary $d$ we explicitly write down the expression for the order $T^{d}$ of the propagator for arbitrary $Δ$, and present a conjecture for the order $T^{2d}$ in the large $Δ$ limit.

hep-th↗

arXiv2021

The free and safe fate of symmetry non-restoration

We investigate the high temperature fate of four dimensional gauge-Yukawa theories featuring short distance conformality of either interacting or non-interacting nature. The latter is known as complete asymptotic freedom and, as templates, we consider non-abelian gauge theories featuring either two singlet scalars coupled to gauged fermions via Yukawa interactions or two gauged scalars with(out) fermions. For theories with interacting fixed points at short distance, known as asymptotically safe, we consider two calculable examples. Exploring the landscape of safe and free theories above we discover a class of complete asymptotically free theories for which symmetry breaks at arbitrary high temperatures. In its minimal form this class is constituted by a theory with two fundamental gauged scalars each gauged under an independent group.

hep-th↗

arXiv2019

Safe Hologram

We introduce a holographic model encapsulating the dynamics of safe quantum field theories.

hep-th↗

arXiv2019

Kutasov-Seiberg dualities and cyclotomic polynomials

We classify all Kutasov-Seiberg type dualities in large $N_c$ SQCD with adjoints of rational $R$-charges. This is done by equating the superconformal index of the electric and magnetic theories: the obtained equation has a solution each time some product of cyclotomic polynomials has only positive coefficients. In this way we easily reproduce without any reference to the superpotential or the choice of the equations of motion (classical chiral ring) all the known dualities from the literature, while adding to them a new family with two adjoints with $R$ charges $\frac{2}{2k+1}$ and $\frac{2(k+1)}{2k+1}$ for all integers $k>1$. We argue that these new fixed points could be in their appropriate conformal windows and in some range of the Yukawas involved a low energy limit of the $D_{2k+2}$ fixed point. We try to clarify some issues connected to the difference between classical and quantum chiral ring of this new solution.

hep-th↗

arXiv2019

Dual RG flows in 4D

We present a prescription for using the a central charge to determine the flow of a strongly coupled supersymmetric theory from its weakly coupled dual. The approach is based on the equivalence of the scale-dependent a-parameter derived from the four-dilaton amplitude with the a-parameter determined from the Lagrange multiplier method with scale-dependent R-charges. We explicitly demonstrate this equivalence for massive free N=1 superfields and for weakly coupled SQCD.

hep-th↗

arXiv2018

Resurrecting Minimal Yukawa Sector of SUSY SO(10)

Supersymmetric $SO(10)$ models with Yukawa coupling matrices involving only a $10_H$ and a $\overline{126}_H$ of Higgs fields can lead to a predictive and consistent scenario for fermion masses and mixings, including the neutrino sector. However, when coupled minimally to a symmetry breaking sector that includes a $210_H$ and a $126_H$, these models lead either to an unacceptably small neutrino mass scale, or to non-perturbative values of the gauge couplings. Here we show that with the addition of a $54_H$ to the symmetry breaking sector, the successful predictions of these models for fermion masses and mixings can be maintained. The $54_H$ enables a reduction of the $B-L$ symmetry breaking scale to an intermediate value of order $10^{12}$ GeV, consistent with the observed neutrino mass spectrum, while preserving perturbative gauge coupling unification. We obtain an excellent fit to all fermion masses and mixings in this framework. We analyze carefully the prediction of the model for CP violation in neutrino oscillations. Consistency with proton lifetime, however, requires a mini-split SUSY spectrum with the squarks and sleptons having masses of order 100 TeV, accompanied by TeV scale gauginos and Higgsinos. Such a spectrum may arise from pure gravity mediation, which would predict the partial lifetime for the decay $p \rightarrow \overlineν K^+$ to be an order of magnitude above the current experimental limit.

hep-ph↗

arXiv2017

Safe SUSY

We investigate the short distance fate of distinct classes of not asymptotically free supersymmetric gauge theories. Examples include super QCD with two adjoint fields and generalised superpotentials, gauge theories without superpotentials and with two types of matter representation and semi-simple gauge theories such as quivers. We show that for the aforementioned theories asymptotic safety is nonperturbatively compatible with all known constraints.

hep-th↗

arXiv2016

Asymptotically Safe Grand Unification

Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.

hep-th↗

arXiv2016

Yukawa Sector of Minimal SO(10) Unification

We show that in SO(10) models, a Yukawa sector consisting of a real $10_H$, a real $120_H$ and a complex $126_H$ of Higgs fields can provide a realistic fit to all fermion masses and mixings, including the neutrino sector. Although the group theory of SO(10) demands that the $10_H$ and $120_H$ be real, most constructions complexify these fields and impose symmetries exterior to SO(10) to achieve predictivity. The proposed new framework with real $10_H$ and real $120_H$ relies only on SO(10) gauge symmetry, and yet has a limited number of Yukawa parameters. Our analysis shows that while there are restrictions on the observables, a good fit to the entire fermion spectrum can be realized. Unification of gauge couplings is achieved with an intermediate scale Pati-Salam gauge symmetry. Proton decay branching ratios are calculable, with the leading decay modes being $p \rightarrow \overlineν π^+$ and $p \rightarrow e^+ π^0$.

hep-ph↗

arXiv2016

Threshold Corrections to Dimension-six Proton Decay Operators in Non-minimal SUSY SU(5) GUTs

We calculate the high and low scale threshold corrections to the D=6 proton decay mode in supersymmetric SU(5) grand unified theories with higher-dimensional representation Higgs multiplets. In particular, we focus on a missing-partner model in which the grand unified group is spontaneously broken by the 75-dimensional Higgs multiplet and the doublet-triplet splitting problem is solved. We find that in the missing-partner model the D=6 proton decay rate gets suppressed by about 60%, mainly due to the threshold effect at the GUT scale, while the SUSY-scale threshold corrections are found to be less prominent when sfermions are heavy.

hep-ph↗

arXiv2016

Hidden flavor symmetries of SO(10) GUT

The Yukawa interactions of the SO(10) GUT with fermions in 16-plets (as well as with singlets) have certain intrinsic ("built-in") symmetries which do not depend on the model parameters. Thus, the symmetric Yukawa interactions of the 10 and 126 dimensional Higgses have intrinsic discrete $Z_2\times Z_2$ symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional Higgs have a continuous SU(2) symmetry. The couplings of SO(10) singlet fermions with fermionic 16-plets have $U(1)^3$ symmetry. We consider a possibility that some elements of these intrinsic symmetries are the residual symmetries, which originate from the (spontaneous) breaking of a larger symmetry group $G_f$. Such an embedding leads to the determination of certain elements of the relative mixing matrix $U$ between the matrices of Yukawa couplings $Y_{10}$, $Y_{126}$, $Y_{120}$, and consequently, to restrictions of masses and mixings of quarks and leptons. We explore the consequences of such embedding using the symmetry group conditions. We show how unitarity emerges from group properties and obtain the conditions it imposes on the parameters of embedding. We find that in some cases the predicted values of elements of $U$ are compatible with the existing data fits. In the supersymmetric version of SO(10) such results are renormalization group invariant.

hep-ph↗

arXiv2016

New Class of SO(10) Models for Flavor

We present a new class of unified models based on SO(10) symmetry which provides insights into the masses and mixings of quarks and leptons, including the neutrinos. The key feature of our proposal is the absence of Higgs boson 10_H belonging to the fundamental representation that is normally employed. Flavor mixing is induced via vector-like fermions in the 16 + 16-bar representation. A variety of scenarios, both supersymmetric and otherwise, are analyzed involving a 126_H along with either a 45_H or a 210_H of Higgs boson employed for symmetry breaking. It is shown that this framework, with only a limited number of parameters, provides an excellent fit to the full fermion spectrum, utilizing either type-I or type-II seesaw mechanism. These flavor models can be potentially tested and distinguished in their predictions for proton decay branching ratios, which are analyzed.

hep-ph↗

arXiv2015

Resurrecting the minimal renormalizable supersymmetric SU(5) model

It is a well-known fact that the minimal renormalizable supersymmetric SU(5) model is ruled out assuming superpartner masses of the order of a few TeV. Giving up this constraint and assuming only SU(5) boundary conditions for the soft terms, we find that the model is still alive. The viable region of the parameter space typically features superpartner masses of order $10^2$ to $10^4$ TeV, with tan beta values between 2 and 5, but lighter spectra with single states around 10 TeV are also possible. The main constraints come from proton decay, the Higgs mass, the requirement of the SU(5) spectrum being reasonably below the Planck scale, and the lifetime of the universe. A generic feature of the model is metastability of the electroweak vacuum. In the absence of a suitable dark matter particle in the neutralino sector, a light (order GeV or smaller) gravitino is a natural candidate.

hep-ph↗