arxiv: 2605.04378 · v1 · submitted 2026-05-06 · ✦ hep-ph · hep-th

Recognition: 5 theorem links

· Lean Theorem

Emergence of conformal properties in Finite Grand Unified Theories via reduction of couplings

Luis Enrique Reyes Rodr\'iguez (Mexico U.) , Myriam Mondrag\'on (Mexico U.)

Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:56 UTC · model grok-4.3

classification ✦ hep-ph hep-th

keywords finite supersymmetric GUTsreduction of couplingsanomaly-mediated supersymmetry breakingno-scale supergravityKähler potentialWeyl invariancesoft supersymmetry breakingconformal regime

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The pith

Reduction of couplings in all-order finite supersymmetric GUTs produces conformal regimes and anomaly-mediated soft terms when the model connects to Weyl-invariant supergravity.

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

The paper demonstrates that Zimmermann's reduction of couplings method, which enforces relations among parameters that remain consistent as the energy scale changes, forces supersymmetric grand unified theories that stay finite to all orders to develop conformal behavior through compatible superpotential operators. In the soft supersymmetry-breaking sector the same relations generate scale-invariant patterns that mirror anomaly-mediated breaking but include a sum rule on scalar masses that prevents tachyonic instabilities. The authors conclude that maintaining all-order finiteness under these conditions requires a particular form of the Kähler potential whose structure matches the one used in no-scale supergravity, provided the grand unified theory is linked to an effective four-dimensional Weyl-invariant supergravity theory. This construction supplies a concrete route to highly predictive, ultraviolet-finite models whose soft parameters are fixed by the same reduction procedure.

Core claim

In supersymmetric GUTs that remain finite to all orders, Zimmermann's Reduction of Couplings applied to the superpotential induces a conformal regime. The same reduction applied to the soft-breaking sector produces a set of scale-invariant relations among soft couplings and dimensionless parameters, including a sum rule for scalar masses that avoids tachyons while reproducing the typical pattern of anomaly-mediated supersymmetry breaking. This pattern emerges only when the finite GUT is assumed to descend from an effective N=1, d=4 Weyl-invariant supergravity theory, and it demands a specific Kähler potential whose form coincides with the one studied in no-scale supergravity scenarios.

What carries the argument

Zimmermann's Reduction of Couplings, which generates renormalization-group-invariant relations among the theory's couplings and thereby enforces conformal properties and soft-term patterns.

If this is right

The superpotential sector develops a conformal regime through operators compatible with the reduction.
Soft-breaking parameters obey scale-invariant relations that resemble anomaly-mediated breaking yet include a scalar-mass sum rule eliminating tachyons.
All-order finite models with these properties require a Kähler potential whose structure is identical to that of no-scale supergravity.
Parameter reduction in the dimensionful soft sector is thereby linked to the emergence of an anomaly-mediated pattern.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Finite GUT constructions may therefore select no-scale Kähler structures automatically once ultraviolet completions are required to preserve all-order finiteness.
The mass sum rule could translate into distinctive, testable correlations among superpartner masses at future colliders.
Analogous reduction mechanisms might apply to other finite supersymmetric models outside the grand-unified setting.

Load-bearing premise

The finite grand unified theory must be connected to an effective N=1, d=4 Weyl-invariant supergravity theory.

What would settle it

An explicit derivation of the Kähler potential for a concrete all-order finite SUSY GUT from a string compactification that fails to match the required no-scale structure while preserving finiteness would falsify the necessity of that form.

read the original abstract

Zimmermann's Reduction of Couplings (RoC) method is a powerful tool for addressing the problem of the excess of parameters in a field theory, as it yields relations among couplings that are invariant under the renormalization group. Its usefulness becomes particularly evident when constructing predictive supersymmetric GUT models that are free of UV-divergences to all orders. Within this scale-invariant framework, we show that a SUSY model satisfying the conditions of all-loop finiteness exhibits a conformal regime induced by superpotential operators compatible with the RoC. In the soft-breaking sector, the method was shown to lead to a set of scale-invariant relations between the soft couplings and the parameters of the dimensionless sector, among which a sum rule for the scalar masses is particularly notable. These relations closely resemble the typical AMSB relations, while avoiding the tachyonic mass spectrum thanks to the sum rule. Based on this observation, we provide new evidence for a connection between the reduction of parameters in the dimensionful SSB sector and the emergence of an anomaly-mediated (AMSB-like) pattern, under the assumption that the finite Grand Unified Theory is connected to an effective $N=1$, $d=4$ Weyl-invariant SUGRA theory. In this process, we find that an all-order finite model with this property requires a specific form of the K\"ahler potential, whose structure coincides with that studied in no-scale supergravity scenarios.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Finite GUTs plus RoC produce conformal and AMSB-like soft terms only after assuming an embedding into Weyl-invariant SUGRA that is not derived from the field theory side.

read the letter

The paper shows that all-loop finite SUSY GUTs, when couplings are reduced via Zimmermann's method, develop a conformal regime from compatible superpotential operators and soft-breaking relations that look like anomaly mediation, complete with a scalar-mass sum rule that sidesteps tachyons. This is presented as new evidence linking parameter reduction in the dimensionful sector to an AMSB-like pattern under the SUGRA assumption, and it points to a no-scale form for the Kähler potential. The observation itself is straightforward and builds directly on prior RoC and finiteness results without introducing unrelated machinery. It gives a concrete handle on how finiteness conditions can constrain soft terms in predictive models. The main limitation is that the requirement for the specific Kähler structure is not obtained from the finite GUT plus RoC conditions alone. It appears only after the authors postulate a connection to an effective N=1, d=4 Weyl-invariant supergravity theory, which supplies the anomaly-mediation structure and the Weyl invariance used to fix the potential. No independent argument is given that finiteness and reduction by themselves force that metric form. The abstract states the outcomes without derivations or explicit checks, so the full text needs to lay out those steps clearly and defend the embedding choice. Readers already working on predictive SUSY GUTs and reduction-of-couplings techniques will find the suggested bridge to no-scale scenarios useful to examine. The paper is worth sending to peer review because the topic matters for BSM model building and the claims are specific enough that referees can test the derivations and the necessity of the SUGRA premise.

Referee Report

2 major / 0 minor

Summary. The manuscript applies Zimmermann's Reduction of Couplings (RoC) to all-order finite supersymmetric GUTs. It claims that such models exhibit a conformal regime from superpotential operators compatible with RoC. In the soft-breaking sector, RoC yields scale-invariant relations among soft parameters that resemble AMSB (including a scalar-mass sum rule preventing tachyons). Under the assumption that the finite GUT connects to an effective N=1, d=4 Weyl-invariant SUGRA theory, the authors conclude that an all-order finite model requires a Kähler potential whose structure coincides with no-scale supergravity scenarios.

Significance. If the embedding assumption holds and the RoC-derived relations are rigorously established, the work would link finite GUT constructions to no-scale SUGRA structures, offering a route to more predictive SUSY models with controlled soft terms. The scalar-mass sum rule that stabilizes the spectrum while preserving AMSB-like features is a concrete positive element. The paper does not supply machine-checked proofs or fully parameter-free derivations, but the explicit identification of the sum rule provides a falsifiable relation that could be tested in specific models.

major comments (2)

[Abstract] Abstract and concluding section: the headline claim that 'an all-order finite model with this property requires a specific form of the Kähler potential' is obtained only after postulating a connection between the finite GUT + RoC framework and an effective Weyl-invariant N=1 SUGRA theory. No independent field-theoretic derivation is given showing that finiteness conditions plus RoC alone force the Kähler metric into the no-scale form; the anomaly-mediation structure and Weyl invariance are supplied by the embedding. This assumption is load-bearing for the central result.
[Soft sector] Soft-breaking sector discussion (likely §3): while the resemblance of the RoC relations to AMSB is asserted and the scalar-mass sum rule is highlighted as avoiding tachyons, the manuscript states these results without explicit derivations, all-order checks, or error estimates. The abstract presents the outcome as established, yet the validity of the sum rule and its exact coefficient cannot be assessed from the given text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We appreciate the positive elements noted regarding the potential significance of linking finite GUTs with RoC to no-scale structures and the falsifiable scalar-mass sum rule. We address each major comment below and will revise the manuscript to improve clarity and completeness.

read point-by-point responses

Referee: [Abstract] Abstract and concluding section: the headline claim that 'an all-order finite model with this property requires a specific form of the Kähler potential' is obtained only after postulating a connection between the finite GUT + RoC framework and an effective Weyl-invariant N=1 SUGRA theory. No independent field-theoretic derivation is given showing that finiteness conditions plus RoC alone force the Kähler metric into the no-scale form; the anomaly-mediation structure and Weyl invariance are supplied by the embedding. This assumption is load-bearing for the central result.

Authors: We agree that the requirement for a no-scale-like Kähler potential is derived under the explicit assumption that the finite GUT connects to an effective N=1, d=4 Weyl-invariant supergravity theory. This assumption is stated in the abstract and is motivated by the emergence of AMSB-like soft-term relations from RoC, which align with the structure of anomaly mediation in Weyl-invariant SUGRA. We do not claim that finiteness and RoC alone, without the embedding, force the Kähler metric into this form; the anomaly-mediation pattern and Weyl invariance are indeed supplied by the SUGRA framework. Our contribution is to show that, within this physically motivated embedding (common in the AMSB and no-scale literature), the RoC conditions select the no-scale structure. To address the concern, we will revise the abstract and concluding section to state the assumption more prominently and add a short paragraph discussing its motivation and scope. revision: yes
Referee: [Soft sector] Soft-breaking sector discussion (likely §3): while the resemblance of the RoC relations to AMSB is asserted and the scalar-mass sum rule is highlighted as avoiding tachyons, the manuscript states these results without explicit derivations, all-order checks, or error estimates. The abstract presents the outcome as established, yet the validity of the sum rule and its exact coefficient cannot be assessed from the given text.

Authors: The RoC relations in the soft sector, including the scalar-mass sum rule, are obtained by applying the reduction conditions to the soft parameters while preserving the scale invariance of the dimensionless sector. These build on all-order results from our prior works on RoC in the SSB sector. The sum rule arises directly from the requirement that the soft masses satisfy the same reduction equations as the gauge and Yukawa couplings, yielding a specific linear combination that eliminates tachyonic directions. We acknowledge that the presentation in §3 is concise and that the abstract states the outcome without sufficient qualifiers. We will expand §3 to include the key algebraic steps deriving the sum rule and its coefficient, cite the all-order RoC proofs explicitly, and adjust the abstract to indicate that the relations follow from the RoC procedure under the stated assumptions. This will allow direct assessment of the coefficient and its validity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; key result is explicitly conditional on an external assumption.

full rationale

The paper states its central claim under the explicit assumption that the finite GUT connects to an effective N=1, d=4 Weyl-invariant SUGRA theory. RoC relations in the soft sector are derived independently and noted to resemble AMSB patterns, after which the no-scale Kähler form is identified as required inside the assumed SUGRA framework. No step reduces a 'prediction' or 'requirement' to a fit or self-definition by construction; the embedding premise is not derived from finiteness + RoC but is instead postulated to interpret the resemblance. Self-citations for prior RoC results are present but not load-bearing for the conditional Kähler conclusion, which remains independent content within the stated assumption.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is limited to the explicit assumption stated there.

axioms (1)

domain assumption The finite Grand Unified Theory is connected to an effective N=1, d=4 Weyl-invariant SUGRA theory
Invoked in the abstract to derive the AMSB-like pattern and the required Kähler form.

pith-pipeline@v0.9.0 · 5562 in / 1319 out tokens · 59840 ms · 2026-05-08T17:56:31.314453+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Cost.FunctionalEquation / Constants washburn_uniqueness_aczel; reality_from_one_distinction echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

Zimmermann's Reduction of Couplings (RoC) method is a powerful tool for addressing the problem of the excess of parameters in a field theory, as it yields relations among couplings that are invariant under the renormalization group.
Cost (J(x) = ½(x+x⁻¹)−1) Jcost ratio-symmetric cost unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

m_i^2 + m_j^2 + m_k^2 = |M|^2 ... model independent ... depends solely on a single parameter, |M|^2.
Foundation (constants forced without SUGRA embedding) reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

an all-order finite model with this property requires a specific form of the Kähler potential, whose structure coincides with that studied in no-scale supergravity scenarios

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

86 extracted references · 46 canonical work pages · 1 internal anchor

[1]

Zimmermann,Reduction in the Number of Coupling Parameters, Commun

W. Zimmermann,Reduction in the Number of Coupling Parameters, Commun. Math. Phys.97(1985) 211

1985
[2]

Zimmermann,Scheme independence of the reduction principle and asymptotic freedom in several couplings, Commun.Math.Phys.219(2001) 221–245

W. Zimmermann,Scheme independence of the reduction principle and asymptotic freedom in several couplings, Commun.Math.Phys.219(2001) 221–245

2001
[3]

Lucchesi, O

C. Lucchesi, O. Piguet and K. Sibold,Necessary and sufficient conditions for all order vanishing beta functions in supersymmetric Yang-Mills theories, Phys. Lett.B201(1988) 241

1988
[4]

Rajpoot and J

S. Rajpoot and J. G. Taylor,On finite quantum field theories, Phys. Lett.B147(1984) 91. 23

1984
[5]

Rajpoot and J

S. Rajpoot and J. G. Taylor,Towards finite quantum field theories, Int. J. Theor. Phys. 25(1986) 117

1986
[6]

Parkes and P

A. Parkes and P. C. West,Finiteness in Rigid Supersymmetric Theories, Phys. Lett. B138(1984) 99

1984
[7]

D. R. T. Jones and L. Mezincescu,The Chiral Anomaly and a Class of Two Loop Finite Supersymmetric Gauge Theories, Phys. Lett. B138(1984) 293–295

1984
[8]

Kapetanakis, M

D. Kapetanakis, M. Mondragon and G. Zoupanos,Finite unified models, Z. Phys.C60 (1993) 181–186 [hep-ph/9210218]

work page arXiv 1993
[9]

Heinemeyer, M

S. Heinemeyer, M. Mondragon and G. Zoupanos,Confronting Finite Unified Theories with Low-Energy Phenomenology, JHEP07(2008) 135 [0712.3630]

work page arXiv 2008
[10]

Heinemeyer, M

S. Heinemeyer, M. Mondragon and G. Zoupanos,Finite Unified Theories and the Higgs boson,1201.5171

work page arXiv
[11]

Heinemeyer, J

S. Heinemeyer, J. Kubo, M. Mondragon, O. Piguet, K. Sibold, W. Zimmermann and G. Zoupanos,Reduction of couplings and its application in particle physics, Finite theories, Higgs and top mass predictions, PoSHiggs and top(2014) 1–339 [1411.7155]

work page arXiv 2014
[12]

Heinemeyer, M

S. Heinemeyer, M. Mondrag´ on, N. Tracas and G. Zoupanos,Reduction of Couplings and its application in Particle Physics, Phys. Rept.814(2019) 1–43 [1904.00410]

work page arXiv 2019
[13]

D. R. T. Jones, L. Mezincescu and Y. P. Yao,Soft breaking of two loop finite N=1 supersymmetric gauge theories, Phys. Lett.B148(1984) 317–322

1984
[14]

Jack and D

I. Jack and D. R. T. Jones,Soft supersymmetry breaking and finiteness, Phys. Lett. B333(1994) 372–379 [hep-ph/9405233]

work page arXiv 1994
[15]

J. Kubo, M. Mondragon and G. Zoupanos,Perturbative unification of soft supersymmetry-breaking terms, Phys. Lett.B389(1996) 523–532 [hep-ph/9609218]

work page arXiv 1996
[16]

Kobayashi, J

T. Kobayashi, J. Kubo, M. Mondragon and G. Zoupanos,Constraints on finite soft supersymmetry breaking terms, Nucl. Phys. B511(1998) 45–68 [hep-ph/9707425]

work page arXiv 1998
[17]

Randall and R

L. Randall and R. Sundrum,Out of this world supersymmetry breaking, Nucl. Phys. B 557(1999) 79–118 [hep-th/9810155]

work page arXiv 1999
[18]

Jack and D

I. Jack and D. R. T. Jones,RG invariant solutions for the soft supersymmetry breaking parameters, Phys. Lett. B465(1999) 148–154 [hep-ph/9907255]

work page arXiv 1999
[19]

Hamidi, J

S. Hamidi, J. Patera and J. H. Schwarz,Chiral two loop finite supersymmetric theories, Phys. Lett.B141(1984) 349

1984
[20]

L. E. Ibanez,A Chiral D = 4, N=1 string vacuum with a finite low-energy effective field theory, JHEP07(1998) 002 [hep-th/9802103]. 24

work page arXiv 1998
[21]

A. E. Lawrence, N. Nekrasov and C. Vafa,On conformal field theories in four-dimensions, Nucl. Phys. B533(1998) 199–209 [hep-th/9803015]

work page arXiv 1998
[22]

Hanany, M

A. Hanany, M. J. Strassler and A. M. Uranga,Finite theories and marginal operators on the brane, JHEP06(1998) 011 [hep-th/9803086]

work page arXiv 1998
[23]

He,Quiver Gauge Theories: Finitude and Trichotomoty, Mathematics6(2018), no

Y.-H. He,Quiver Gauge Theories: Finitude and Trichotomoty, Mathematics6(2018), no. 12 291

2018
[24]

D. R. T. Jones and S. Raby,A two loop finite supersymmetric SU(5) theory: towards a theory of fermion masses, Phys. Lett.B143(1984) 137

1984
[25]

J. Kubo, M. Mondragon and G. Zoupanos,Reduction of couplings and heavy top quark in the minimal SUSY GUT, Nucl. Phys. B424(1994) 291–307

1994
[26]

E. Ma, M. Mondragon and G. Zoupanos,Finite SU(N)**k unification, JHEP12(2004) 026 [hep-ph/0407236]

work page arXiv 2004
[27]

Superconformal Inflationary $\alpha$-Attractors

R. Kallosh, A. Linde and D. Roest,Superconformal Inflationaryα-Attractors, JHEP11 (2013) 198 [1311.0472]

work page Pith review arXiv 2013
[28]

Ellis, M

J. Ellis, M. A. G. Garcia, D. V. Nanopoulos and K. A. Olive,No-Scale Inflation, Class. Quant. Grav.33(2016), no. 9 094001 [1507.02308]

work page arXiv 2016
[29]

R2-inflation derived from 4d strings, the role of the dilaton, and turning the Swampland into a mirage,

I. Antoniadis, D. V. Nanopoulos and K. A. Olive,R 2-inflation derived from 4d strings, the role of the dilaton, and turning the Swampland into a mirage, JHEP06(2025) 155 [2410.16541]

work page arXiv 2025
[30]

Oehme and W

R. Oehme and W. Zimmermann,Relation Between Effective Couplings for Asymptotically Free Models, Commun. Math. Phys.97(1985) 569

1985
[31]

Oehme,Reduction and Reparametrization of Quantum Field Theories, Prog

R. Oehme,Reduction and Reparametrization of Quantum Field Theories, Prog. Theor. Phys. Suppl.86(1986) 215

1986
[32]

J. Kubo, K. Sibold and W. Zimmermann,Higgs and Top Mass from Reduction of Couplings, Nucl.Phys.B259(1985) 331

1985
[33]

J. Kubo, K. Sibold and W. Zimmermann,New Results in the Reduction of the Standard Model, Phys. Lett. B220(1989) 185–190

1989
[34]

Decker and J

R. Decker and J. Pestieau,Lepton self-mass, Higgs scalar and heavy quark masses, in DESY Workshop 1979: Quarks, Jets and QCD, 1979.hep-ph/0512126

work page arXiv 1979
[35]

Chaichian, R

M. Chaichian, R. Gonzalez Felipe and K. Huitu,On quadratic divergences and the Higgs mass, Phys. Lett. B363(1995) 101–105 [hep-ph/9509223]

work page arXiv 1995
[36]

Pendleton and G

B. Pendleton and G. G. Ross,Mass and Mixing Angle Predictions from Infrared Fixed Points, Phys. Lett. B98(1981) 291–294. 25

1981
[37]

Zimmermann,Infrared behaviour of the coupling parameters in the standard model, Physics Letters B308(1993), no

W. Zimmermann,Infrared behaviour of the coupling parameters in the standard model, Physics Letters B308(1993), no. 1-2 117–122

1993
[38]

M. T. Grisaru, D. I. Kazakov and D. Zanon,Five Loop Divergences for theN= 2 Supersymmetric NonlinearσModel, Nucl. Phys. B287(1987) 189

1987
[39]

D. I. Kazakov and L. V. Bork,Conformal invariance = finiteness and beta deformed N=4 SYM theory, JHEP08(2007) 071 [0706.4245]

work page arXiv 2007
[40]

The Power of holomorphy: Exact results in 4-D SUSY field theories,

N. Seiberg,The Power of holomorphy: Exact results in 4-D SUSY field theories, in Particles, Strings, and Cosmology (PASCOS 94), pp. 0357–369, 5, 1994. hep-th/9408013

work page internal anchor Pith review arXiv 1994
[41]

Piguet and K

O. Piguet and K. Sibold,Nonrenormalization theorems of chiral anomalies and finiteness, Phys. Lett.B177(1986) 373

1986
[42]

Lucchesi, O

C. Lucchesi, O. Piguet and K. Sibold,Vanishing beta functions in N=1 supersymmetric gauge theories, Helv. Phys. Acta61(1988) 321

1988
[43]

Lucchesi and G

C. Lucchesi and G. Zoupanos,All order finiteness in N=1 SYM theories: Criteria and applications, Fortsch. Phys.45(1997) 129–143 [hep-ph/9604216]

work page arXiv 1997
[44]

Piguet and K

O. Piguet and K. Sibold,Nonrenormalization Theorems of Chiral Anomalies and Finiteness in Supersymmetric Yang-Mills Theories, Int. J. Mod. Phys. A1(1986) 913

1986
[45]

Piguet and K

O. Piguet and K. Sibold,The Supercurrent inN= 1Supersymmetrical Yang-Mills Theories. 1. The Classical Case, Nucl. Phys. B196(1982) 428–446

1982
[46]

Piguet and K

O. Piguet and K. Sibold,The Supercurrent inN= 1Supersymmetrical Yang-Mills Theories. 2. Renormalization, Nucl. Phys. B196(1982) 447–460

1982
[47]

M. A. Shifman and A. I. Vainshtein,Solution of the Anomaly Puzzle in SUSY Gauge Theories and the Wilson Operator Expansion, Nucl. Phys. B277(1986) 456

1986
[48]

Cordova, T

C. Cordova, T. T. Dumitrescu and K. Intriligator,Multiplets of Superconformal Symmetry in Diverse Dimensions, JHEP03(2019) 163 [1612.00809]

work page arXiv 2019
[49]

R. G. Leigh and M. J. Strassler,Exactly marginal operators and duality in four-dimensional N=1 supersymmetric gauge theory, Nucl. Phys. B447(1995) 95–136 [hep-th/9503121]

work page arXiv 1995
[50]

Ferrara and B

S. Ferrara and B. Zumino,Transformation Properties of the Supercurrent, Nucl. Phys. B 87(1975) 207

1975
[51]

M. T. Grisaru, B. Milewski and D. Zanon,Supercurrents, Anomalies and the Adler-bardeen Theorem, Phys. Lett. B157(1985) 174–178. 26

1985
[52]

Blumenhagen and E

R. Blumenhagen and E. Plauschinn, Introduction to conformal field theory: with applications to String theory, vol. 779. 2009

2009
[53]

Gukov,Counting RG flows, JHEP01(2016) 020 [1503.01474]

S. Gukov,Counting RG flows, JHEP01(2016) 020 [1503.01474]

work page arXiv 2016
[54]

Conformal manifolds: ODEs from OPEs

C. Behan,Conformal manifolds: ODEs from OPEs, JHEP03(2018) 127 [1709.03967]

work page Pith review arXiv 2018
[55]

Hisano and M

J. Hisano and M. A. Shifman,Exact results for soft supersymmetry breaking parameters in supersymmetric gauge theories, Phys. Rev.D56(1997) 5475–5482 [hep-ph/9705417]

work page arXiv 1997
[56]

I. Jack, D. R. T. Jones and A. Pickering,Renormalisation invariance and the soft beta functions, Phys. Lett.B426(1998) 73–77 [hep-ph/9712542]

work page arXiv 1998
[57]

Fujikawa and W

K. Fujikawa and W. Lang,Perturbation Calculations for the Scalar Multiplet in a Superfield Formulation, Nucl. Phys.B88(1975) 61

1975
[58]

M. T. Grisaru, W. Siegel and M. Rocek,Improved Methods for Supergraphs, Nucl. Phys. B159(1979) 429

1979
[59]

Kobayashi, J

T. Kobayashi, J. Kubo and G. Zoupanos,Further all-loop results in softly-broken supersymmetric gauge theories, Phys. Lett.B427(1998) 291–299 [hep-ph/9802267]

work page arXiv 1998
[60]

Vandoren and P

S. Vandoren and P. van Nieuwenhuizen,Lectures on instantons,0802.1862

work page arXiv
[61]

Brignole, L

A. Brignole, L. E. Ibanez, C. Munoz and C. Scheich,Some issues in soft SUSY breaking terms from dilaton / moduli sectors, Z.Phys.C74(1997) 157–170 [hep-ph/9508258]

work page arXiv 1997
[62]

Kawamura, T

Y. Kawamura, T. Kobayashi and J. Kubo,Soft scalar-mass sum rule in gauge-yukawa unified models and its superstring interpretation, Physics Letters B405(1997), no. 1-2 64–70

1997
[63]

Gherghetta, G

T. Gherghetta, G. F. Giudice and J. D. Wells,Phenomenological consequences of supersymmetry with anomaly induced masses, Nucl. Phys. B559(1999) 27–47 [hep-ph/9904378]

work page arXiv 1999
[64]

G. F. Giudice, M. A. Luty, H. Murayama and R. Rattazzi,Gaugino mass without singlets, JHEP12(1998) 027 [hep-ph/9810442]

work page arXiv 1998
[65]

D. J. H. Chung, L. L. Everett, G. L. Kane, S. F. King, J. D. Lykken and L.-T. Wang, The Soft supersymmetry breaking Lagrangian: Theory and applications, Phys. Rept.407 (2005) 1–203 [hep-ph/0312378]

work page arXiv 2005
[66]

Luty and Valentina Prilepina,Weyl versus Conformal Invariance in Quantum Field Theory,JHEP10(Oct., 2017) 170, [arXiv:1702.07079pdf], [Inspire]

K. Farnsworth, M. A. Luty and V. Prilepina,Weyl versus Conformal Invariance in Quantum Field Theory, JHEP10(2017) 170 [1702.07079]

work page arXiv 2017
[67]

D. V. Nanopoulos,The March towards no scale supergravity, NATO Sci. Ser. B352 (1996) 677–693 [hep-ph/9411281]. 27

work page arXiv 1996
[68]

Kaplunovsky and J

V. Kaplunovsky and J. Louis,Field dependent gauge couplings in locally supersymmetric effective quantum field theories, Nuclear Physics B422(1994), no. 1-2 57–124

1994
[69]

Ellis, A

J. Ellis, A. B. Lahanas, D. V. Nanopoulos, M. Quiros and F. Zwirner,Supersymmetry breaking in the observable sector of superstring models, Physics Letters B188(1987), no. 4 408–414

1987
[70]

S. J. G. Jr, M. T. Grisaru, M. Rocek and W. Siegel,Superspace, or one thousand and one lessons in supersymmetry, 2001

2001
[71]

Cheung, F

C. Cheung, F. D’Eramo and J. Thaler,Supergravity Computations without Gravity Complications, Phys. Rev. D84(2011) 085012 [1104.2598]

work page arXiv 2011
[72]

Salam and J

A. Salam and J. Strathdee,Superfields and fermi-bose symmetry, Physical Review D11 (1975), no. 6 1521

1975
[73]

J. R. Ellis, J. S. Hagelin, D. V. Nanopoulos, K. A. Olive and M. Srednicki, Supersymmetric relics from the big bang, Nucl. Phys.B238(1984) 453–476

1984
[74]

J. R. Ellis, C. Kounnas and D. V. Nanopoulos,No Scale Supersymmetric Guts, Nucl. Phys. B247(1984) 373–395

1984
[75]

Y. Ema, M. A. G. Garcia, W. Ke, K. A. Olive and S. Verner,Inflaton Decay in No-Scale Supergravity and Starobinsky-like Models, Universe10(2024), no. 6 239 [2404.14545]

work page arXiv 2024
[76]

Boyda, H

E. Boyda, H. Murayama and A. Pierce,DREDed anomaly mediation, Phys. Rev. D65 (2002) 085028 [hep-ph/0107255]

work page arXiv 2002
[77]

Arkani-Hamed, G

N. Arkani-Hamed, G. F. Giudice, M. A. Luty and R. Rattazzi,Supersymmetry breaking loops from analytic continuation into superspace, Phys. Rev. D58(1998) 115005 [hep-ph/9803290]

work page arXiv 1998
[78]

M. T. Grisaru and D. Zanon,NEW, IMPROVED SUPERGRAPHS, Phys. Lett. B142 (1984) 359–364

1984
[79]

Arkani-Hamed and H

N. Arkani-Hamed and H. Murayama,Holomorphy, rescaling anomalies and exact beta functions in supersymmetric gauge theories, JHEP06(2000) 030 [hep-th/9707133]

work page arXiv 2000
[80]

B. J. Warr,Renormalization of Gauge Theories Using Effective Lagrangians. 1., Annals Phys.183(1988) 1

1988

Showing first 80 references.