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REVIEW 3 major objections 5 minor 44 references

Holography for QCD(Adj) and QCD(Adj)+F

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper argues that in adjoint-plus-fundamental gauge theories, chiral symmetry breaking can take place an order of magnitude above the confinement scale, and builds holographic models that predict the mass gap.

desk verdict A transparent, self-aware bottom-up holographic model paper that unifies instanton and fermion condensation via BF bounds; the numbers are extrapolations, but the lattice-facing gap prediction is worth referee time. read the letter →

arxiv 2506.09456 v1 pith:RMKXXBXS submitted 2025-06-11 hep-th hep-lathep-ph

Anja Alfano , Nick Evans , Wanxiang Fan This is my paper
classification hep-thhep-lathep-ph MSC 81T3581T1381V05 PACS 11.25.Tq12.38.Aw12.38.Lg
keywords holographicQCDadjointfermionschiralsymmetrybreakingconfinementBFboundinstantoncondensationconformalwindowlatticeprediction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether confinement and chiral symmetry breaking can occur at different energy scales in SU(Nc) gauge theories with adjoint fermions. It builds holographic models for both mechanisms: instanton/monopole condensation on a compact circle drives confinement through a Breitenlohner-Freedman (BF) bound violation, while fermion bilinear condensation drives chiral symmetry breaking through the same type of instability when the anomalous dimension crosses one. The paper then adds fundamental fermions to slow the running of the gauge coupling, and finds that the separation between the two scales can grow to about an order of magnitude, with the largest predicted gap in SU(5) near seventeen fundamental flavours where the adjoint and fundamental rho meson masses differ by a factor of about 12. The point of the exercise is to give lattice simulations a concrete target: a large scale gap would show that chiral symmetry breaking can precede confinement, while its absence would support the view that the two phenomena are tied together.

What carries the argument

The load-bearing device is the Breitenlohner-Freedman bound used as a universal trigger for condensation: a bulk scalar whose mass squared falls below the AdS bound becomes unstable and condenses, which in field theory language is the $\gamma = 1$ criterion for fermion bilinears and the instanton-density analogue for monopoles. For the instanton field in AdS$_4$ the paper uses a running mass $M_I^2 = -K/r$ with $r^2 = \rho^2 + I^{2/3}$, so the bound is violated only in the infrared and the growing condensate back-reacts to restabilise the solution. For the fermion sectors it uses $\Delta m^2 = -2\gamma$ with $\gamma = 3C_2(R)/(2\pi)\alpha$, the running of $\alpha$ fixed by the two-loop $\beta$ function, and all spectra normalised to the adjoint rho meson mass to remove the choice of initial coupling.

What would settle it

A lattice simulation of SU(5) with one Weyl adjoint and about seventeen fundamental Dirac flavours could measure the adjoint-to-fundamental rho mass ratio and the temperatures of the chiral and deconfinement transitions; a ratio near one with coincident transitions would falsify the predicted order-of-magnitude gap, and even an intermediate ratio would already discriminate between the extrapolation choices.

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Extended reading notes

Core claim

On the paper's own terms, both the condensation of magnetically charged instantons and the condensation of fermion bilinears are BF bound violations, and a single holographic language can describe both. In the compactified strongly coupled SU(2) adjoint theory, the instanton density field $I$ condenses when its effective mass squared crosses the AdS$_4$ BF bound $M_I^2 = -9/4$, producing a spectrum of instanton-density fluctuations with masses squared $1.56$, $4.36$, $9.52$; the dual photon $\sigma$ becomes massive through the monopole potential, and the model even recognises parameter regimes where the three-dimensional description should fail. The adjoint fermion bilinear is described in AdS$_5$ by a running $\Delta m^2 = -2\gamma$, so chiral symmetry breaking switches on when $\gamma = 1$. A very naive perturbative extrapolation puts this fermion-driven instability at slightly weaker coupling than the instanton-driven one, so chiral symmetry breaking may happen before confinement. Adding $N_f^F$ fundamental Dirac fermions slows the running after the adjoint sector condenses, and the model predicts adjoint-to-fundamental rho mass ratios of up to $12.38$ for SU(5) near $N_f^F = 17$, with maximum ratios of $10.63$ (SU(3), $N_f^F = 10$), $8.50$ (SU(4), $N_f^F = 13$), and $5.26$ (SU(2), $N_f^F = 6$).

Load-bearing premise

The quantitative predictions depend on extending the perturbative two-loop $\beta$ function and the one-loop relation $\gamma = 3C_2(R)/(2\pi)\alpha$ into the strongly coupled regime where the condensation actually happens; the paper states explicitly that this is 'an extrapolation of the perturbative results that favours early condensation and hence larger gaps.'

Editorial extensions

If this is right

  • In the compactified SU(2) adjoint theory, the holographic instanton-density fluctuations have masses squared $1.56$, $4.36$, $9.52$, and the dual photon spectrum depends on $g_4$, with tachyonic modes appearing exactly in the parameter regimes where the three-dimensional description should break down.
  • The same BF-bound comparison places the adjoint fermion instability at $g_4^2 = 6.6$ for $N_c = 2$, slightly before the estimated instanton condensation scale, so chiral symmetry breaking may precede confinement rather than being caused by it.
  • Adding fundamental flavours is predicted to enlarge the separation, up to about a factor of 12 in SU(5) near $N_f^F = 17$, with order-of-magnitude gaps generically possible near the edge of the conformal window.
  • The adjoint sigma meson becomes very light as the conformal window edge is approached, a walking signature in the adjoint sector whenever the gap is large.
  • If the predictions are right, lattice studies should find separate scales for chiral restoration and deconfinement in these theories; the existing SU(2) lattice data point with an adjoint-to-fundamental rho ratio near 1.6 is consistent with the model but far from the maximal gap.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the predicted gaps should be read as upper bounds, because the paper itself states that its extrapolation 'favours early condensation and hence larger gaps'; a lattice null result would therefore constrain the extrapolation scheme rather than the general idea of separated scales.
  • Because the model omits cross-couplings between the adjoint, fundamental, and instanton sectors, the cleanest test is not the mass ratio alone but whether the chiral and deconfinement transitions occur at distinct temperatures; if they never separate in any lattice theory, the $\gamma = 1$ separation picture itself is under pressure.
  • The same machinery points to near-conformal walking theories with a light composite scalar (the adjoint sigma) as natural places where a light scalar coexists with a large separation of scales, which would matter for technicolor-style model building if the gap is real.
  • The $N = 1$ super Yang-Mills limit with no fundamentals is a calibration point: there the glueballs and gaugino bound states sit in a single supermultiplet, so any realistic dynamics must make the gap shrink as the theory approaches pure adjoint matter, a trend the model already shows at smaller $N_c$.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes holographic models for SU(Nc) gauge theories with adjoint fermions, compactified on a circle of radius L, and for the same theories with additional fundamental fermions. On the confinement side, an AdS4 model with a scalar sigma and an instanton-density field I describes the strong-coupling regime of the compactified theory; a BF-bound violation in the I sector is identified with instanton condensation, and fluctuation spectra are computed. On the chiral side, an AdS5 model follows the running anomalous dimension gamma of fermion bilinears and triggers condensation when the BF bound is violated. For QCD(Adj)+F, the model predicts that the adjoint fermions condense at a higher scale than the fundamentals, generating mass gaps between adjoint and fundamental mesons that can be as large as an order of magnitude (e.g., SU(5), Nf about 17). The paper presents numerical solutions for embeddings, spectra, and decay constants, and frames the results as a challenge to lattice simulations.

Significance. If the proposed models are valid, the paper offers a unified holographic language in which both instanton condensation (confinement) and chiral symmetry breaking are driven by BF-bound violations, and it makes quantitative, falsifiable predictions for the relative scales of the two phenomena and for meson mass ratios in QCD(Adj)+F. The strengths of the paper are the explicit numerical construction of the vacuum and fluctuation solutions, the computed spectra and decay constants across Nc and Nf, and the candid acknowledgment of the speculative extrapolations involved. The significance is conditional: the AdS4 action is posited by analogy with D3/probe-D7, and the central predictions inherit the uncertainty of extending perturbative running to strong coupling. The existence of a large gap in SU(5) with Nf about 17 is the kind of prediction lattice studies could in principle test, which motivates publication after the internal consistency issues are resolved.

major comments (3)
  1. [Section IV, Eqs. (29)-(30), and Section V.A, Eq. (34)] The paper uses two incompatible BF-violation thresholds. Equation (29) gives Delta M^2 = gamma(gamma-2), whose AdS5 BF violation occurs at Delta M^2 = -1, i.e., gamma = 1, as stated in Section IV. However, Eq. (30) and Section V.A use the linearized relation Delta M^2 = -2 gamma, for which the BF bound is reached at gamma = 1/2; this is exactly the criterion stated in Section V.A ('The model breaks chiral symmetry when gamma passes 1/2'). The numerical values in Section IV, g4^2 = 6.6 for Nc = 2 and g4^2 = 4.4 for Nc = 3, follow from gamma = 1/2 with gamma = 3 C2(R)/(2 pi) alpha, not from gamma = 1; with gamma = 1 they would be g4^2 = 4 pi^2/3 about 13.2 and g4^2 = 8 pi^2/9 about 8.8, respectively. The manuscript must specify which mass-dimension relation defines the model and recompute the affected scales accordingly.
  2. [Section IV, paragraph beginning 'In competition with this instanton-driven...'] The qualitative ordering of the two instabilities is reversed by the threshold ambiguity. For Nc = 2 the instanton-condensation scale is quoted as g4^2 about 7.7. With the gamma = 1/2 convention actually used in the numerics, the fermion-condensation scale (g4^2 about 6.6) precedes it, supporting the abstract's suggestion that chiral symmetry breaking may occur first. With the gamma = 1 criterion stated in the text, the fermion scale (g4^2 about 13.2) lies above the instanton scale, so confinement would precede chiral symmetry breaking. Since the abstract and conclusions rely on this ordering, a consistent comparison is required before the claim is supported.
  3. [Section V.B.1 and Figure 5] The headline result of an order-of-magnitude gap for SU(5) with Nf about 17 is an artifact of the gamma = 1/2 threshold. For Nf = 16.9 the adjoint sector has Delta m^2 about -1.04 in the IR, i.e., gamma about 0.52, which is just above the gamma = 1/2 threshold but far below the gamma = 1 threshold. Under the gamma = 1 criterion of Section IV, the adjoint operator would not violate the BF bound at this Nf, and the large gap shown in Figure 7 and quoted as about 12.38 would not occur. The authors need to either justify the gamma = 1/2 extrapolation as the model's non-perturbative choice or provide the analogous computation under the gamma = 1 criterion; the current version cannot support both conventions.
minor comments (5)
  1. [Abstract and Section IV] Breitenlohner-Freedman is misspelled as 'Brietenlohner-Freedman' in the abstract and in Section IV.
  2. [Section III.B and III.C] Typographical errors: 'it's example' should be 'its example' and 'daigonalized' should be 'diagonalized'.
  3. [Section V.B.2] The sentence 'The results are shown in Figure 8' should refer to Figure 9, which contains the SU(2), SU(3), and SU(4) spectra and decay constants; Figure 8 displays the SU(5) decay constants.
  4. [Section IV and Section V.A] The notation for the gauge coupling is inconsistent: the text uses g4, g2_4, and g4^2 in close proximity. Since the instanton action is S0 = 4 pi^2 / g4^2, the coupling convention should be defined once and used uniformly.
  5. [Equations (29) and (30)] Both equations use the symbol Delta M^2 for different quantities: the exact AdS mass relation and its linearized small-gamma approximation. Distinguishing these would prevent the threshold ambiguity documented in the major comments.

Circularity Check

4 steps flagged · score 6.0 of 10

The gap and ordering 'predictions' are read off the input running at a threshold chosen to favor them; Section IV's quoted couplings use γ=1/2 despite stating γ=1, the instanton BF scale is tuned to the field theory input, and the central premise is inherited from the authors' prior model.

  1. self definitional [Section V.A, 'The Holographic Model' (Eqs. 34-37), and Figure 5; Section V.B.1]
    "We use the perturbative result for the running of the anomalous dimension of the quark mass, γ and expand M 2 = ∆(∆ − 4) at small γ giving ∆m2 = −2γ. ... Since the true running of γ is not known non-perturbatively, we extend the perturbative results ... The model breaks chiral symmetry when γ passes 1/2, as the BF bound is then violated. This is an extrapolation of the perturbative results that favours early condensation and hence larger gaps."

    The condensation ('on-shell') scale for each representation is defined as where the input one-loop γ(µ)=3C2(R)α(µ)/(2π), run from the input two-loop beta function with the chosen α(1)=0.65, crosses the chosen threshold γ=1/2. The headline gap (SU(5), Nf≈17: adjoint BF violation at ln µ=13.9, fundamental at ln µ=−2.2, rho-mass ratio ≈12) is therefore the separation between two crossings of the same running curve that was put in; there is no independent datum fixing the non-perturbative continuation, and the result could not have contradicted the ansatz. The paper's own admission that the extrapolation 'favours early condensation and hence larger gaps' makes explicit that the order-of-magnitude claim is a consequence of the input choice, not an output of the model.

  2. self definitional [Section IV, after Eq. (30); cross-referenced with Section V.A]
    "There is a BF bound violation that causes gaugino condensation when γ = 1 (∆ M 2 = −1). ... ∆M 2 = −2γ, γ = 3C2(R)/(2π) α (30) ... This BF bound violation is now predicted to occur at g 2 4 = 6.6 for Nc = 2 and g 2 4 = 4.4 for Nc = 3. ... The model breaks chiral symmetry when γ passes 1/2, as the BF bound is then violated."

    Substituting γ=1 into Eq. (30) for Nc=2 gives g²4 = 8π²/(3C2) = 4π²/3 ≈ 13.2, not the quoted 6.6; 6.6 is the γ=1/2 value (2π²/3), and Section V.A confirms the model triggers at γ=1/2. The abstract's suggestion that chiral symmetry breaking 'might occur ahead of confinement' rests on this unadvertised half-threshold: with the paper's stated γ=1 criterion the quoted instanton scale g²4=7.7 precedes the fermion scale 13.2, reversing the ordering. The claimed ordering is thus fixed by which threshold is inserted into the same input running, i.e., the conclusion is constructed rather than derived.

2 more flagged steps
  1. renaming known result [Section III.B, 'From Weak to Strong Coupling with Holography']
    "Now we must decide on a form for the mass squared for I. We want a running mass (i.e. a ρ dependent mass) that will violate the BF bound in the IR causing condensation of I - we will adjust the BF bound violation point so that the condensation occurs to match that expected in the field theory model."

    The AdS4 instanton model's BF-violation scale is tuned: K=7.82498 is chosen so the I solution tends to I=1 in the UV, and I=1 is identified with the field theory input 4e^{−S0}/L³. The derived scale ρ_BF=3.47(4e^{−S0}/L³)^{1/3} and the 'instanton condensation' coupling g²4=7.7 are then the field theory instanton action re-expressed in holographic units. The Section IV comparison of this scale with the adjoint-fermion γ threshold is consequently a comparison of two inputs (the e^{−S0} instanton density and the extrapolated one-loop running), with the model contributing only an overall constant. The glueball spectrum (1.56, 4.36, 9.52) is a genuine model output, so this step is partial.

  2. self citation load bearing [Section I, Introduction; Section V.B.1, 'Nc = 5 Theory']
    "In a previous paper [23], we built a holographic model of SU(Nc) theories with two-index symmetric matter and fundamentals which displayed such gaps. ... Here we use the same model for SU(Nc) with a single Weyl adjoint fermion and N F f fundamentals ... In [8] this model was identified as having a maximum gap between the condensation scales of the representations at N F f = 17."

    The premise that adding fundamentals enlarges the chiral-confinement gap, and the showcase parameter choice, are imported from the authors' own prior work: the model equations from [23] ('The full equations can be found in [23]') and the maximal-gap expectation with the SU(5), Nf=17 selection from [8]. Both [8] and [23] use the same extrapolated one-loop γ and the same holographic ansatz, so the self-citation chain is load-bearing for the central claim. The new SU(2,3,4,5) spectra and decay constants are genuine recomputations within the stated model, and one external lattice study [31] is cited for qualitative consistency, so this step contributes partial rather than total circularity.

full rationale

The paper is a deliberately 'straw-man' holographic model study, and it explicitly disclaims first-principles status ('very naively extending the perturbative results', 'intended to provoke first principle lattice simulations'). That transparency does not, however, remove the structural circularity in the central claims. In Section V the chiral-symmetry-breaking scale of each representation is defined as where the input one-loop anomalous dimension γ(µ)=3C2(R)α(µ)/2π, integrated from the input two-loop beta function with chosen α(1)=0.65, crosses the chosen threshold γ=1/2; the advertised 'gaps as big as an order of magnitude' are the separations of those crossing points (or the meson masses they seed), so the output is the input running rearranged. The paper concedes the extrapolation 'favours early condensation and hence larger gaps', confirming that the result is tuned by construction. Second, the Section IV comparison of fermion versus instanton condensation is internally inconsistent: the text announces the γ=1 criterion, but the quoted couplings (g²4=6.6 for Nc=2, 4.4 for Nc=3) are the γ=1/2 values from Eq. (30) (γ=1 would give 4π²/3≈13.2 and 8π²/9≈8.8); under the stated criterion the instanton scale 7.7 precedes the fermion scale, reversing the abstract's suggestion. Third, the model's instanton BF scale is tuned ('we will adjust the BF bound violation point so that the condensation occurs to match that expected in the field theory model'), so the instanton-vs-fermion comparison re-expresses inputs rather than deriving from them. Fourth, the premise that a gap can exist and the showcase SU(5), Nf=17 case come from the authors' own [8], computed with the same model as [23]. Because the headline results reduce to the assumed running, the chosen threshold, and the tuned BF point, I assign 6. There is independent content (new meson spectra and decay constants, one cited lattice consistency check [31]), so this is partial rather than total circularity.

Assumptions & free parameters 5 free parameters · 6 assumptions · 2 invented entities

The model rests on the assumption that bottom-up AdS/QCD rules apply to the strongly coupled IR of compactified adjoint theories. The central dynamics are set by free inputs: K and rho_IR fix the instanton condensation scale; alpha(1)=0.65 and the extrapolated one-loop gamma formula fix where fermion condensation occurs; the interpolation between runnings is unspecified. The AdS4 action is posited by D3/D7 analogy, not derived. The paper is transparent about these choices, but they mean the 'predictions' are consequences of the assumed running and model parameters rather than independent derivations.

free parameters (5)
  • K = 7.82498
    Sets the running mass squared M_I^2 = -K/r for the instanton density operator I in the AdS4 model; tuned so the UV solution satisfies I(rho_UV)=1 with I'(rho_UV)=0 (Section III.B).
  • rho_IR = 0.223527
    IR on-shell boundary for the I equation; determined together with K by the shooting conditions in Eq. (15) and fixes the instanton condensation scale.
  • alpha(1) = 0.65
    Initial coupling for the two-loop running in the QCD(Adj)+F model (Section V.A). The paper rewrites results in units of the adjoint rho mass, but the gap itself depends on the running and hence on this input.
  • N_f = 16.9 = 16.9 (approximating 17)
    Used in the SU(5) numerics because N_f=17 is described as numerically intractable; the gap is then extrapolated to the edge of the conformal window.
  • Interpolation between adjoint-coupled and adjoint-decoupled runnings = Not specified
    In Section V.B.1 the running of Delta m^2_F transitions from the full theory to the adjoint-decoupled theory via 'an interpolation function'; its form is not given and affects the fundamental BF bound scale.
assumptions (6)
  • domain assumption AdS/CFT-style duality applies to the strongly coupled IR of the compactified SU(Nc) adjoint theory.
    Section III.B: 'In this regime, one can propose a holographic description of the strongly coupled sigma-instanton bath system.' This is assumed, not derived.
  • domain assumption BF bound violation is the correct trigger for both instanton condensation and fermion condensation.
    Used throughout the paper as the organizing principle; the paper does not justify why this criterion remains valid in the strongly coupled regime beyond the standard AdS dictionary.
  • ad hoc to paper The perturbative two-loop beta function and one-loop anomalous dimension relation gamma = 3 C2(R)/(2 pi) alpha can be extrapolated to strong coupling.
    Section V.A: 'Since the true running of gamma is not known non-perturbatively, we extend the perturbative results...' This extrapolation directly sets the BF bound violation scales and the size of the predicted gap.
  • ad hoc to paper D3/probe D7 boundary conditions and the back-reaction replacement r^2 = rho^2 + I^(2/3) transfer to the AdS4 instanton model.
    Section III.B: 'Although this choice looks a little arbitrary, the D3/probe D7 system artfully enables this from first principles - we follow it's example.'
  • ad hoc to paper The field theory RG scale mu equals the holographic RG scale r = sqrt(rho^2 + |X_R|^2).
    Section V.A: 'We then directly set the field theory RG scale mu equal to the holographic RG scale r.' This identification is not derived.
  • domain assumption Interactions between the adjoint, fundamental, and instanton sectors can be neglected.
    Section I: 'We also neglect interactions between the two fermionic sectors... condensation in one could trigger condensation in the other, for example, undoing the conclusions.'
invented entities (2)
  • I(rho,x): dimension-3 instanton density operator in AdS4
    purpose: Represents the density of magnetically charged instanton configurations whose vev 4 exp(-S0)/L^3 triggers confinement; its fluctuations give glueball-like bound states.
    No independent falsifiable handle outside the model; the mass spectrum M_I^2 = 1.56, 4.36, 9.52 is a prediction of the model, not a measured quantity.
  • sigma-hat(rho,x): holographic dual of the compactified dual-photon scalar sigma
    purpose: Describes the electric flux tube and dual photon degrees of freedom and the instanton-induced potential; its mass spectrum is computed as a function of g4.
    The weakly coupled sigma field is known from the compactified theory, but the strong-coupling holographic description is not derived, so the entity has no independent evidence beyond the model's internal consistency.

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Cite this review

Pith. "Pith review of Holography for QCD(Adj) and QCD(Adj)+F." pith.science (2026). https://pith.science/paper/RMKXXBXS

@misc{pith2026250609456,
  author       = {Pith},
  title        = {Pith review of: Holography for QCD(Adj) and QCD(Adj)+F},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RMKXXBXS}},
  note         = {Machine review of arXiv:2506.09456}
}
read the original abstract

We discuss confinement and chiral symmetry breaking in SU(Nc) gauge theories with fermions in the adjoint representation. There has been considerable work on studying these theories compactified on a small circle (with compactification scale 1/L large relative to the strong coupling scale of the theory). The weakly coupled IR theory of photons exhibits confinement through a density of magnetically charged instanton configurations. As the compactification scale 1/L approaches the strong coupling scale, the IR theory becomes strongly coupled. In this regime we propose a holographic description of the IR degrees of freedom. The instanton condensation scale can be associated with a scale at which the Brietenlohner-Freedman (BF) bound is violated in the model and the glueball spectrum computed. We can also introduce the adjoint fermions which holographically display a BF bound violation associated to their running anomalous dimension. Very naively extending the perturbative results to the non-perturbative regime suggests that chiral symmetry breaking might occur ahead of confinement, but equally they may be joined phenomena. If the two phenomena are separate, then it would be useful to be able to enlarge the gap in scales. We propose adding fermions in the fundamental representation as well, which in a holographic model (that favours this separation) can greatly enlarge the gap to an order of magnitude. These results challenge the lattice community to seek such scale gaps (or their absence) to further understand the confining and chiral symmetry breaking dynamics.

Figures

Figures reproduced from arXiv: 2506.09456 by the authors.

Figure 1
Figure 1. Top: The blue line is the numerical result for [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Top: The regular solutions for the fluctuation of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. The mass spectrum of dual photons σ1 and σ2 for SU(3). The darker colours represent σ1; The lighter colours represent σ2. C. The SU(Nc) Theory The SU(Nc) theory with adjoint matter (which we again assume is massive, but with those masses below the com￾pactification scale) shows similar behaviour [15, 16]. The A3 component of the gauge field again becomes an adjoint scalar on compactification and its vev breaks the t… view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: SU(5) gauge theory with one Weyl adjoint [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 7
Figure 7. Figure 7: Mass spectra for the SU(5) theory, ρ-mesons in blue (adjoint) and dark yellow (fundamental), σ-mesons in green (adjoint) and orange (fundamental), axials in purple (adjoint) and brown (fundamental). The pions in both sectors are massless at zero fermion mass [PITH_FUL…
Figure 8
Figure 8. Figure 8: Decay constants for the SU(5) theory, ρ-mesons in blue (adjoint) and dark yellow (fundamental), σ-mesons in green (adjoint) and orange (fundamental), axials in purple (adjoint) and brown (fundamental) and pions in cyan (adjoint) and light yellow (fundamental). For the …
Figure 9
Figure 9. Figure 9: The spectra and decay constants of the SU(N [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

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