Topological couplings in higher derivative extensions of supersymmetric three-form gauge theories

Abstract We investigate the relation between $S$-matrix unitarity ($SS^\dagger=1$) and renormalizability in theories with negative-norm states. The relation has been confirmed in many field theories, including gauge theories and Einstein gravity, by analyzing the unitarity bound, which follows from the $S$-matrix unitarity and the norm positivity. On the other hand, renormalizable theories with a higher-derivative kinetic term do not necessarily satisfy the unitarity bound because of the negative-norm states. In these theories it is not known whether the $S$-matrix unitarity provides a nontrivial constraint related to the renormalizability. In this paper, by relaxing the assumption of norm positivity we derive a bound on scattering amplitudes weaker than the unitarity bound, which may be used as a consistency requirement for $S$-matrix unitarity. We demonstrate in scalar field models with a higher-derivative kinetic term that the weaker bound and the renormalizability imply identical constraints.

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Asymptotic freedom and higher derivative gauge theories

Journal of High Energy Physics ◽

10.1007/jhep05(2021)075 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

M. Asorey ◽

F. Falceto ◽

L. Rachwał

Keyword(s):

Gauge Theories ◽

Asymptotic Freedom ◽

Effective Masses ◽

Small Family ◽

High Energies ◽

Strongly Interacting ◽

Higher Derivative

Abstract The ultraviolet completion of gauge theories by higher derivative terms can dramatically change their behavior at high energies. The requirement of asymptotic freedom imposes very stringent constraints that are only satisfied by a small family of higher derivative theories. If the number of derivatives is large enough (n > 4) the theory is strongly interacting both at extreme infrared and ultraviolet regimes whereas it remains asymptotically free for a low number of extra derivatives (n ⩽ 4). In all cases the theory improves its ultraviolet behavior leading in some cases to ultraviolet finite theories with vanishing β-function. The usual consistency problems associated to the presence of extra ghosts in higher derivative theories may not harm asymptotically free theories because in that case the effective masses of such ghosts are running to infinity in the ultraviolet limit.

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HIGGS MECHANISM FOR GRAVITONS

Modern Physics Letters A ◽

10.1142/s0217732310033724 ◽

2010 ◽

Vol 25 (28) ◽

pp. 2411-2421 ◽

Cited By ~ 14

Author(s):

ICHIRO ODA

Keyword(s):

Cosmological Constant ◽

Gauge Theories ◽

Minkowski Spacetime ◽

Scalar Fields ◽

Higgs Mechanism ◽

Spacetime Dimension ◽

Gauge Bosons ◽

Higher Derivative ◽

Vector Gauge ◽

Arbitrary Potential

Just like the vector gauge bosons in the gauge theories, it is now known that gravitons acquire mass in the process of spontaneous symmetry breaking of diffeomorphisms through the condensation of scalar fields. The point is that we should find the gravitational Higgs mechanism such that it results in massive gravity in a flat Minkowski spacetime without non-unitary propagating modes. This is usually achieved by including higher-derivative terms in scalars and tuning the cosmological constant to be a negative value in a proper way. Recently, a similar but different gravitational Higgs mechanism has been advocated by Chamseddine and Mukhanov where one can relax the negative cosmological constant to zero or positive one. In this work, we investigate why the non-unitary ghost mode decouples from physical Hilbert space in a general spacetime dimension. Moreover, we generalize the model to possess an arbitrary potential and clarify under what conditions the general model exhibits the gravitational Higgs mechanism. By searching for solutions to the conditions, we arrive at two classes of potentials exhibiting gravitational Higgs mechanism. One class includes the model by Chamseddine and Mukhanov in a specific case while the other is a completely new model.

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Subleading corrections to the S3 free energy of necklace quiver theories dual to massive IIA

Journal of High Energy Physics ◽

10.1007/jhep11(2021)183 ◽

2021 ◽

Vol 2021 (11) ◽

Author(s):

Junho Hong ◽

James T. Liu

Keyword(s):

Free Energy ◽

Partition Function ◽

Gauge Theories ◽

Fermi Gas ◽

Tree Level ◽

Saddle Point Approximation ◽

Higher Derivative ◽

The Matrix ◽

Hooft Limit ◽

Chern Simons

Abstract We investigate the S3 free energy of $$ \mathcal{N} $$ N = 3 Chern-Simons-matter quiver gauge theories with gauge group U(N)r (r ≥ 2) where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-N limit. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the ’t Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy F = − log Z are then compared in the overlapping parameter regime. The Fermi-gas approach also hints at a universal $$ \frac{1}{6} $$ 1 6 log N correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect the sub-leading correction of the planar free energy in the large ’t Hooft parameter limit to match higher-derivative corrections to the tree-level holographic dual free energy, which have not yet been fully investigated.

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