Remark on the consistent gauge anomaly in supersymmetric theories

Ohshima, Yoshihisa; Okuyama, Kiyoshi; Suzuki, Hiroshi; Yasuta, Hirofumi

doi:10.1016/s0370-2693(99)00585-7

Cited by 12 publications

(16 citation statements)

References 40 publications

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“…The superfield version of the covariant anomaly is straightforward, A cov ∝ d 4 x d 2 θtr iΛW α W α + h.c., where W α denotes the nonabelian superfield vector field strength and Λ is a chiral superfield. 6 Supersymmetric expressions for the difference between the consistent and covariant anomaly for a simple gauge group are complicated [30,31,32,33]. Some simplication occurs for the mixed U(1) − G 2 abelian anomaly which can be obtained from [30,31] and written as…”

Section: Supersymmetrizationmentioning

confidence: 99%

Anomaly cancellation in supergravity with Fayet-Iliopoulos couplings

Elvang

Freedman

Körs

2006

J. High Energy Phys.

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We review and clarify the cancellation conditions for gauge anomalies which occur when N = 1, D = 4 supergravity is coupled to a Kähler non-linear sigma-model with gauged isometries and Fayet-Iliopoulos couplings. For a flat sigma-model target space and vanishing Fayet-Iliopoulos couplings, consistency requires just the conventional anomaly cancellation conditions. A consistent model with non-vanishing Fayet-Iliopoulos couplings is unlikely unless the Green-Schwarz mechanism is used. In this case the U(1) gauge boson becomes massive and the D-term potential receives corrections. A Green-Schwarz mechanism can remove both the abelian and certain non-abelian anomalies in models with a gauge non-invariant Kähler potential.

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Section: Supersymmetrizationmentioning

confidence: 99%

Anomaly cancellation in supergravity with Fayet-Iliopoulos couplings

Elvang

Freedman

Körs

2006

J. High Energy Phys.

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“…which ensures the cancellation of the gauge anomalies [116,117]. Below we will always assume that this condition is valid.…”

Section: The Theory Under Consideration: Action Regularization and Qu...mentioning

confidence: 99%

Finiteness of the triple gauge-ghost vertices in $${{\mathcal {N}}}=1$$ supersymmetric gauge theories: the two-loop verification

et al. 2022

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By an explicit calculation we demonstrate that the triple gauge-ghost vertices in a general renormalizable $${{\mathcal {N}}}=1$$ N = 1 supersymmetric gauge theory are UV finite in the two-loop approximation. For this purpose we calculate the two-loop divergent contribution to the $$\bar{c}^+ V c$$ c ¯ + V c -vertex proportional to $$(C_2)^2$$ ( C 2 ) 2 and use the finiteness of the two-loop contribution proportional to $$C_2 T(R)$$ C 2 T ( R ) which has been checked earlier. The theory under consideration is regularized by higher covariant derivatives and quantized in a manifestly $${{\mathcal {N}}}=1$$ N = 1 supersymmetric way with the help of $${{\mathcal {N}}}=1$$ N = 1 superspace. The two-loop finiteness of the vertices with one external line of the quantum gauge superfield and two external lines of the Faddeev–Popov ghosts has been verified for a general $$\xi $$ ξ -gauge. This result agrees with the nonrenormalization theorem proved earlier in all orders, which is an important step for the all-loop derivation of the exact NSVZ $$\beta $$ β -function.

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“…Moreover, the product of two such propagators is also proportional to Q −2 due to Eq. (70). That is why the terms proportional to Q µ /Q 4 (where Q µ is a momentum of the matter superfield) can appear only if the operator (γ µ )ȧ b θ bDȧ D 2 /∂ 2 acts on the matter propagator (from the right) or stands between two matter propagators with the same momenta, 9…”

Section: C2 Terms Quadratic In the Matter Superfieldsmentioning

confidence: 99%

The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities

Stepanyantz

2020

J. High Energ. Phys.

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The contributions of the matter superfields and of the Faddeev-Popov ghosts to the βfunction of N = 1 supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the higher covariant derivative regularization. For this purpose we use the recently proved statement that the β-function in these theories is given by integrals of double total derivatives with respect to the loop momenta. These integrals do not vanish due to singularities of the integrands. This implies that the β-function beyond the one-loop approximation is given by the sum of the singular contributions, which is calculated in all orders for singularities produced by the matter superfields and by the Faddeev-Popov ghosts. The result is expressed in terms of the anomalous dimensions of these superfields. It coincides with the corresponding part of the new form of the NSVZ equation, which can be reduced to the original one with the help of the non-renormalization theorem for the triple gauge-ghost vertices.

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Remark on the consistent gauge anomaly in supersymmetric theories

Cited by 12 publications

References 40 publications

Anomaly cancellation in supergravity with Fayet-Iliopoulos couplings

Anomaly cancellation in supergravity with Fayet-Iliopoulos couplings

Finiteness of the triple gauge-ghost vertices in $${{\mathcal {N}}}=1$$ supersymmetric gauge theories: the two-loop verification

The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities

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