{"arxiv_id":"hep-th/0304128","incoming":{"papers":267,"sentences":417,"groups":[{"kind":"extends","label":"Builds on it","papers":2,"sentences":3,"quotes":[{"arxiv_id":"2101.12648","title":"Defect $a$-Theorem and $a$-Maximization","url":"/paper/2101.12648","section":"Introduction and Summary","sentence":"Furthermore in the presence of 4d conserved currents on the defect, we prove a defect version of the $a$-maximization principle [ref] (see also [ref] ) that identifies the superconformal $U(1)_R$ symmetry as a linear combination that may involve these 4d currents.","intent_p":0.96,"contests_p":null},{"arxiv_id":"2012.06574","title":"Surface Defect, Anomalies and $b$-Extremization","url":"/paper/2012.06574","section":"Defects of dimensions $p≠2$","sentence":"The $a$-maximization principle of [ref] also has a natural extension to the superconformal defect similar to what we studied here [ref] .","intent_p":0.92,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":110,"sentences":155,"quotes":[{"arxiv_id":"1307.7104","title":"Linear Quivers and N=1 SCFTs from M5-branes","url":"/paper/1307.7104","section":"Central charges and $R$-symmetry","sentence":"The superconformal R-symmetries maximizes the function $a(ϵ)$ and thus uniquely determines the value of $ϵ$ [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"1106.5051","title":"New dynamics and dualities in supersymmetric chiral gauge theories","url":"/paper/1106.5051","section":"$a$-maximization in the electric theory","sentence":"The superconformal R-charges are determined by extremizing the $a$-function [ref] a = 332(2 (N^2 -1)+N(N+3) f(R_Q) + N f(R_P) +N (2N-2) f(R_Q) + 12N(N-1)f(R_A) ) , where the first term is the contribution from the gauginos, and f(R_O) = 3(R_O-1)^3 - (R_O-1) .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1806.08353","title":"Landscape of Simple Superconformal Field Theories in 4d","url":"/paper/1806.08353","section":"A Landscape of Simple SCFTs","sentence":"We employ the $a$-maximization procedure [ref] and its modification [ref] to compute the superconformal $R$-charges at each step.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1107.4101","title":"Invariants of Toric Seiberg Duality","url":"/paper/1107.4101","section":"Dimer models and Seiberg duality","sentence":"As the IR superconformal $R$-symmetry is visible in the UV, we can thus identify it using the standard $a$-maximization algorithm[ In fact, that no accidental $U(1)$s mixing with the $U(1)_R$ appear along the flow is implicitly assumed everywhere in the literature, as it is required to use the machinery of [ref] .] and trace it back to UV.","intent_p":0.97,"contests_p":null},{"arxiv_id":"1611.01229","title":"4d SCFTs from negative-degree line bundles","url":"/paper/1611.01229","section":"Construction of $C_g>1,n=0$ and computation of $a$ and $c$","sentence":"Then, the exact superconformal R-symmetry at an IR fixed point is determined by $a$-maximization with respect to $ϵ$ [ref] .","intent_p":0.97,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2607.28143","title":"Interior zeros of supersymmetric indices","url":"/paper/2607.28143","section":"4d $𝒩=1$ $SU(2)$ gauge theories","sentence":"The chiral multiplets have superconformal R-charge $1-2/N_f$ [ref] .","intent_p":0.89,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":5,"sentences":5,"quotes":[{"arxiv_id":"1603.08935","title":"Relevant deformations and c-extremization","url":"/paper/1603.08935","section":"Conclusions","sentence":"We have shown that with our assumptions there is a simplification in the c-extremization of [ref] , and the two-dimensional R-symmetry is determined much as in N=1 d=4 flows, which maximize a trial function for the central charge $a$ [ref] .","intent_p":0.82,"contests_p":null},{"arxiv_id":"2505.10626","title":"$\\mathcal{I}$-Extremization for AdS$_4$ Black Holes: Master Volume, Free Energy, and Baryonic Charges","url":"/paper/2505.10626","section":"Comparing with the quantum field theory free energy","sentence":"As a non-trivial check, we now show that the extremization of $_2 n-1(Δ_a)$ reproduces the correct exact R-symmetry and is consistent with what we know about $a$- and $F$-maximization [ref] and their equivalence with volume minimization [ref] .","intent_p":0.89,"contests_p":null},{"arxiv_id":"1204.6085","title":"The Lightest Higgs Boson Mass in the MSSM with Strongly Interacting Spectators","url":"/paper/1204.6085","section":"Model Near the Conformal Fixed Point","sentence":"To justify our use of the one-loop anomalous dimensions, let us compare our one-loop approximation with the anomalous dimensions determined non-perturbatively using $a$-maximization [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"2403.02410","title":"Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography","url":"/paper/2403.02410","section":"$a$-maximization and the large-$N$ expansion","sentence":"Substituting its value into the first equation, we arrive at [equation] which just says that [equation] in agreement with [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"2604.15420","title":"Local CFTs extremise $F$","url":"/paper/2604.15420","section":"Definitions and disambiguations","sentence":"Our story is very similar to that of supersymmetric $$-extremisation (also called $c,F,a$-maximisation in $d=2,3,4$ [ref] ), although admittedly less powerful.","intent_p":0.9,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":53,"sentences":55,"quotes":[{"arxiv_id":"1706.03346","title":"Machine Learning of Calabi-Yau Volumes","url":"/paper/1706.03346","section":"Volume Minimization and the AdS/CFT correspondence","sentence":"The superconformal R-charges of the theory are determined by a procedure known as $a$-maximization [ref] , which involves the maximization of the $a$-charge, es20 a(R; Y) = 3/32 (3Tr R^3 - Tr R) . $a$-maximization gives the value of the central charge at the conformal fixed point, which is by the AdS/CFT correspondence related to the volume minimum of the corresponding Sasaki-Einstein 5-manifold [ref] under es21 a(R; Y) = π^3 N^2/4 V(R;Y) , where the R-charge $R$ can be expressed in terms of Reeb vector components $b_i$.","intent_p":0.86,"contests_p":null},{"arxiv_id":"1104.5490","title":"The Beta Ansatz: A Tale of Two Complex Structures","url":"/paper/1104.5490","section":"Conclusion","sentence":"It was observed that the isoradial embedding of the dimer [ref] provides another complex structure $τ_R$ for the torus after $a$-maximization [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"2511.22546","title":"Holographic origin of $a$-maximization and higher-derivative AdS$_5$/CFT$_4$","url":"/paper/2511.22546","section":"Introduction","sentence":"This procedure is the gravitational analog of $a$-maximization [ref] , which in field theory determines the exact superconformal R-symmetry by maximizing the trial $a$-anomaly over all possible R-symmetry mixings.","intent_p":0.82,"contests_p":null},{"arxiv_id":"1901.05977","title":"Proving the equivalence of $c$-extremization and its gravitational dual for all toric quivers","url":"/paper/1901.05977","section":"Introduction","sentence":"It is well known that, for $N=1$ supersymmetric theories in four dimensions, the extremization of a trial central charge $a$ with respect to a varying R-symmetry allows to identify the exact R-symmetry of the superconformal theory [ref] .[The exact R-symmetry is the one appearing in the superconformal algebra.] Similarly, for $= (0,2)$ supersymmetric theories in two dimensions, the extremization of a right-moving trial central charge $c_r$ allows to identify the exact R-symmetry [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2012.06574","title":"Surface Defect, Anomalies and $b$-Extremization","url":"/paper/2012.06574","section":"Holographic dual of $b$-extremization and $b$-anomalies","sentence":"The $c$-extremization principle of 2d $=(0,2)$ SCFTs [ref] has an elegant geometric dual in the context of AdS/CFT [ref] , in terms of extremizing certain functionals of off-shell geometries in string/M/F-theory (in close analogy to the holographic dual of $a$-maximization [ref] developed in [ref] ).","intent_p":0.9,"contests_p":null}]}],"unlabelled_sentences":198},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":{"arxiv_id":"hep-th/0304128","kind":"model","paper_version":3,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T13:38:22+00:00","loaded_at":"2026-10-28T01:01:56.514848+00:00","evidence":"substantial","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":22,"entries":[{"p":1.0,"quote":null,"citing":[{"self":false,"year":2013,"title":"Linear Quivers and N=1 SCFTs from M5-branes","arxiv_id":"1307.7104"}],"verified":true,"paraphrase":"Used knowledge of the global symmetries together with a-maximization as its main calculation tool."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2018,"title":"Landscape of Simple Superconformal Field Theories in 4d","arxiv_id":"1806.08353"}],"verified":true,"paraphrase":"Employed the a-maximization procedure and its modification to compute the superconformal R-charges at each step."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2020,"title":"SQCD and pairs of pants","arxiv_id":"2006.03480"}],"verified":true,"paraphrase":"Computed the superconformal R-symmetry by a-maximization with these interactions and obtained that the 6d R-symmetry is now the superconformal one."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2018,"title":"4D Gauge Theories with Conformal Matter","arxiv_id":"1803.00582"}],"verified":true,"paraphrase":"Maximized a(ϵ), so that a-maximization fixes the value of ϵ, and plugged that value in to get a and c."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2017,"title":"The $AdS_5$ non-Abelian T-dual of Klebanov-Witten as a $\\mathcal{N} = 1$ linear quiver from M5-branes","arxiv_id":"1705.09661"}],"verified":true,"paraphrase":"Computed the central charge of the quiver at the fixed point using the a-maximization procedure."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2019,"title":"Symmetry enhancement in 4d Spin(n) gauge theories and compactification from 6d","arxiv_id":"1910.03629"}],"verified":true,"paraphrase":"Used a maximization to find that U(1)_r̂ is the superconformal R charge and the conformal anomalies are a=123/64 and c=163/64."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2021,"title":"Infinitely many 4d N=1 SCFTs with a=c","arxiv_id":"2111.12092"}],"verified":true,"paraphrase":"Performed a-maximization to determine the superconformal R-symmetry at the end of the RG flow."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2023,"title":"Supersymmetric Cardy Formula and the Weak Gravity Conjecture in AdS/CFT","arxiv_id":"2308.01717"}],"verified":true,"paraphrase":"Imposed the anomaly-free condition and used the a-maximization procedure to find the superconformal R-charges at IR."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2010,"title":"Cascade supersymmetry breaking and low-scale gauge mediation","arxiv_id":"1009.2818"}],"verified":true,"paraphrase":"Used an a-maximization method to do so."},{"p":1.0,"quote":{"text":"At each step, we employ $a$-maximization [ref] and its modification [ref] to compute the superconformal R-charges.","citing":"2408.02953","section":"Deforming $𝒩=1$ SCFT"},"citing":[{"self":false,"year":2024,"title":"Large Landscape of 4d Superconformal Field Theories from Small Gauge Theories","arxiv_id":"2408.02953"}],"verified":true,"paraphrase":"Employed a-maximization and its modification at each step to compute the superconformal R-charges."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2017,"title":"Asymptotic safety guaranteed in supersymmetry","arxiv_id":"1709.06953"}],"verified":true,"paraphrase":"Found non-perturbative expressions for the R-charges using the method of a-maximisation."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2017,"title":"RG flows with supersymmetry enhancement and geometric engineering","arxiv_id":"1710.06469"}],"verified":true,"paraphrase":"Started by applying the method proposed by Maruyoshi and Song and identified the chiral operators violating the unitarity bound in the IR with a run of a-maximization."},{"p":0.99,"quote":null,"citing":[{"self":false,"year":2011,"title":"New dynamics and dualities in supersymmetric chiral gauge theories","arxiv_id":"1106.5051"}],"verified":true,"paraphrase":"Determined the superconformal R-charges by extremizing the a-function."},{"p":0.97,"quote":null,"citing":[{"self":false,"year":2011,"title":"Invariants of Toric Seiberg Duality","arxiv_id":"1107.4101"}],"verified":true,"paraphrase":"Identified the IR superconformal R-symmetry using the standard a-maximization algorithm and traced it back to UV."},{"p":0.97,"quote":null,"citing":[{"self":false,"year":2016,"title":"4d SCFTs from negative-degree line bundles","arxiv_id":"1611.01229"}],"verified":true,"paraphrase":"Determined the exact superconformal R-symmetry at an IR fixed point by a-maximization with respect to ϵ."},{"p":0.99,"quote":null,"citing":[{"self":false,"year":2016,"title":"Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index","arxiv_id":"1606.05632"}],"verified":true,"paraphrase":"Used a-maximization and its modification as the key ingredient in the analysis."},{"p":0.99,"quote":null,"citing":[{"self":false,"year":2023,"title":"BBBW on the spindle","arxiv_id":"2309.11362"}],"verified":true,"paraphrase":"Found the exact superconformal R-symmetry by a-maximization, since the abelian symmetries mix together."},{"p":0.95,"quote":null,"citing":[{"self":false,"year":2009,"title":"Superconformal Flavor Simplified","arxiv_id":"0910.4585"}],"verified":true,"paraphrase":"Pointed out that a-maximization is precisely the needed method to determine the correct superconformal U(1)_R-symmetry."},{"p":0.99,"quote":null,"citing":[{"self":false,"year":2017,"title":"Lagrangians for generalized Argyres-Douglas 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A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"21 later papers by other authors are listed below: 21 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool."},"_links":{"html":"https://pith.science/paper/hep-th/0304128"}}