Δa curiosities in some 4d susy RG flows

Amariti, Antonio; Intriligator, Kenneth

doi:10.1007/jhep11(2012)108

Cited by 11 publications

(13 citation statements)

References 60 publications

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“…We collectively refer to such topological relations as the "µ-theorem", even though in practice it often involves not only the index (1.5) but also topology of conformal manifolds at the fixed points and other data. Notice, our proposal for the piecewise structure of the gradient flow fits well with the known properties of 2d RG flows [3,8] and 4d N = 1 flows [9,26]. In particular, the "branch flip" in a-maximization is precisely an example of such "phase transition" and non-smooth behavior of the a-function.…”

Section: Introductionsupporting

confidence: 74%

“…Therefore, we find another interesting example of dangerously irrelevant operators and a topological obstruction to the strongest form of the C-theorem. Incidentally, precisely this type of behavior, where a double-trace operator crosses through marginality is known [26] to cause the "branch flip" in a-maximization and is responsible for non-smooth behavior of the a-function under RG flow. This strongly suggests that a violation of (1.6)-(1.8) is indeed a signal for violation of the strongest form of the C-theorem, and that "phase transitions" along such N = 1 RG flows are of second order.…”

Section: Now Let Us Consider Some Interesting Examples With Dangerousmentioning

confidence: 99%

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Counting RG flows

Gukov

2016

J. High Energ. Phys.

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Interpreting renormalization group flows as solitons interpolating between different fixed points, we ask various questions that are normally asked in soliton physics but not in renormalization theory. Can one count RG flows? Are there different "topological sectors" for RG flows? What is the moduli space of an RG flow, and how does it compare to familiar moduli spaces of (supersymmetric) dowain walls? Analyzing these questions in a wide variety of contexts -from counting RG walls to AdS/CFT correspondence -will not only provide favorable answers, but will also lead us to a unified general framework that is powerful enough to account for peculiar RG flows and predict new physical phenomena. Namely, using Bott's version of Morse theory we relate the topology of conformal manifolds to certain properties of RG flows that can be used as precise diagnostics and "topological obstructions" for the strong form of the C-theorem in any dimension. Moreover, this framework suggests a precise mechanism for how the violation of the strong C-theorem happens and predicts "phase transitions" along the RG flow when the topological obstruction is non-trivial. Along the way, we also find new conformal manifolds in well-known 4d CFT's and point out connections with the superconformal index and classifying spaces of global symmetry groups.

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Section: Introductionsupporting

confidence: 74%

Section: Now Let Us Consider Some Interesting Examples With Dangerousmentioning

confidence: 99%

Counting RG flows

Gukov

2016

J. High Energ. Phys.

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“…Sharper upper bounds for scaling dimensions in SCFTs have been studied in [35,36]. In the case where we take into account wave-function renormalization effects, we can also calculate the leading order shift to T :…”

Section: Weakly Coupled Modelsmentioning

confidence: 99%

Oblique electroweak parametersSandTfor superconformal field theories

2013

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We develop a general set of methods for computing the oblique electroweak parameters S and T for bottom-up and top-down motivated scenarios in which the Higgs weakly mixes with a superconformal extra sector. In addition to their utility in phenomenological studies, the observables S and T are also of purely theoretical interest as they are defined by correlation functions of broken symmetries. We show that in the limit where the extra sector enjoys an approximate custodial symmetry, the leading contributions to S and T can be recast as calculable data of the theory in the conformal phase. Using this result, we also obtain model-independent bounds on the sign and size of oblique electroweak corrections from unitary superconformal theories.

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“…More precisely, we will show that-under reasonable assumptions-for RG flows with N = 2 SUSY at least one of the following applies (i) δa > ∆ univ > 0. 9 In [39], the authors discussed RG flows with δa = 0 and so we should interpret δa as a measure of the length of the RG flow with care. For our purposes here, we simply note that the δa = 0 RG flows of [39] are special in the sense that they can be understood as being initiated by giving vevs to scalars that only interact with the UV SCFT via highly irrelevant operators.…”

Section: Introductionmentioning

confidence: 99%

“…9 In [39], the authors discussed RG flows with δa = 0 and so we should interpret δa as a measure of the length of the RG flow with care. For our purposes here, we simply note that the δa = 0 RG flows of [39] are special in the sense that they can be understood as being initiated by giving vevs to scalars that only interact with the UV SCFT via highly irrelevant operators. In particular, turning on these vevs does not generate relevant deformations of the UV theory.…”

Section: Introductionmentioning

confidence: 99%

Minimal distances between SCFTs

Buican

2014

J. High Energ. Phys.

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Abstract:We study lower bounds on the minimal distance in theory space between four-dimensional superconformal field theories (SCFTs) connected via broad classes of renormalization group (RG) flows preserving various amounts of supersymmetry (SUSY). For N = 1 RG flows, the ultraviolet (UV) and infrared (IR) endpoints of the flow can be parametrically close. On the other hand, for RG flows emanating from a maximally supersymmetric SCFT, the distance to the IR theory cannot be arbitrarily small regardless of the amount of (non-trivial) SUSY preserved along the flow. The case of RG flows from N = 2 UV SCFTs is more subtle. We argue that for RG flows preserving the full N = 2 SUSY, there are various obstructions to finding examples with parametrically close UV and IR endpoints. Under reasonable assumptions, these obstructions include: unitarity, known bounds on the c central charge derived from associativity of the operator product expansion, and the central charge bounds of Hofman and Maldacena. On the other hand, for RG flows that break N = 2 → N = 1, it is possible to find IR fixed points that are parametrically close to the UV ones. In this case, we argue that if the UV SCFT possesses a single stress tensor, then such RG flows excite of order all the degrees of freedom of the UV theory. Furthermore, if the UV theory has some flavor symmetry, we argue that the UV central charges should not be too large relative to certain parameters in the theory.

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Δa curiosities in some 4d susy RG flows

Cited by 11 publications

References 60 publications

Counting RG flows

Counting RG flows

Oblique electroweak parametersSandTfor superconformal field theories

Minimal distances between SCFTs

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