Lagrange multipliers and couplings in supersymmetric field theory

Kutasov, David; Schwimmer, A.

doi:10.1016/j.nuclphysb.2004.10.030

Cited by 58 publications

(104 citation statements)

References 14 publications

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“…This discussion is very similar the one performed in [5] in the case of AdS 5 gauged supergravity, and it has an interesting connection with the results obtained on the field theory side in [27,28]. We remark here that in 4D SCFTs the effect of the broken symmetries is captured in the context of a-maximization by including Lagrange multipliers in the extremization procedure.…”

Section: Jhep07(2016)006supporting

confidence: 83%

3D τ RR -minimization in AdS4 gauged supergravity

Amariti

Gnecchi

2016

J. High Energ. Phys.

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In this paper we propose the identification in AdS 4 N = 2 gauged supergravity of the coefficient τ RR of 3D N = 2 SCFTs. We constrain the structure of this function in supergravity by combining the results from unitarity, holography and localization. We show that our conjectured function is minimized by the exact R-charge, corresponding to a gravitational attractor for the scalars of special geometry. We identify this mechanism with the supergravity dual of τ RR -minimization. We check this proposal in ABJM model, comparing with expectations from localization and AdS/CFT duality. We comment also on possible relations with black hole microstates counting, recently obtained from application of localization techniques.

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Section: Jhep07(2016)006supporting

confidence: 83%

3D τ RR -minimization in AdS4 gauged supergravity

Amariti

Gnecchi

2016

J. High Energ. Phys.

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“…Moreover, here it was possible to show that an exact formula for the a-function conjectured in refs. [20][21][22][23][24] was valid at this order; in previous work [25] this had been checked at the level of the two-loop β-functions for a general, gauged N = 1 supersymmetric theory (in the rest of this paper we shall describe this as a "two-loop check" although the corresponding a-function is actually a four-loop quantity). A sufficient condition on the chiral field anomalous dimension for this exact a-function to be viable was presented and shown (using the results of ref.…”

Section: Jhep01(2015)138mentioning

confidence: 99%

“…[25] (and is hence compatible with ref. [20][21][22][23][24]). Finally, again in the context of supersymmetry, we extend the condition on the chiral superfield anomalous…”

Section: Jhep01(2015)138mentioning

confidence: 99%

The a-function for gauge theories

Jack

Poole

2015

J. High Energ. Phys.

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Abstract:The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the β-functions via a gradient flow equation involving a positive definite metric. We construct the a-function at four-loop order for a general gauge theory with fermions and scalars, using only one and two loop β-functions; we are then able to provide a stringent consistency check on the general three-loop gauge β-function. In the case of an N = 1 supersymmetric gauge theory, we present a general condition on the chiral field anomalous dimension which guarantees an exact all-orders expression for the a-function; and we verify this up to fifth order (corresponding to the three-loop anomalous dimension).

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“…13 A chiral operator is marginal at the interacting fixed point if its total r-charge is 2. So the r-charges have to satisfy the following 3 linear relations, analogous of (3.7): Once this equation is satisfied, we can reconstruct uniquely the 4-vector of the ranks in terms of the quiver matrix, and we can also find the 6 r-charges.…”

Section: Jhep04(2006)032mentioning

confidence: 99%

“…K 2 = 12 − (α + β + γ) for del Pezzo quivers K 2 = 9 − (α + β + γ) for the "new" quivers (A. 13) relating K 2 to the total number of nodes.…”

Section: Jhep04(2006)032mentioning

confidence: 99%

New results on superconformal quivers

Benvenuti¹,

Hanany²

2006

J. High Energy Phys.

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All superconformal quivers are shown to satisfy the relation c = a and are thus good candidates for being the field theory living on D3 branes probing CY singularities. We systematically study 3 block and 4 block chiral quivers which admit a superconformal fixed point of the RG equation. Most of these theories are known to arise as living on D3 branes at a singular CY manifold, namely complex cones over del Pezzo surfaces. In the process we find a procedure of getting a new superconformal quiver from a known one. This procedure is termed "shrinking" and, in the 3 block case, leads to the discovery of two new models. Thus, the number of superconformal 3 block quivers is 16 rather than the previously known 14. We prove that this list exausts all the possibilities. We suggest that all rank 2 chiral quivers are either del Pezzo quivers or can be obtained by shrinking a del Pezzo quiver and verify this statement for all 4 block quivers, where a lot of "shrunk" del Pezzo models exist.

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Lagrange multipliers and couplings in supersymmetric field theory

Cited by 58 publications

References 14 publications

3D τ RR -minimization in AdS4 gauged supergravity

3D τ RR -minimization in AdS4 gauged supergravity

The a-function for gauge theories

New results on superconformal quivers

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