DOCSLIB.ORG

Renormalizability of Super Yang–Mills Theory in Landau Gauge with A

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Renormalizability of Super Yang–Mills Theory in Landau Gauge with A Eur. Phys. J. C (2018) 78:797 https://doi.org/10.1140/epjc/s10052-018-6239-5 Regular Article - Theoretical Physics Renormalizability of N = 1 super Yang–Mills theory in Landau gauge with a Stueckelberg-like field M. A. L. Capria, D. M. van Egmondb, M. S. Guimaraesc, O. Holandad, S. P. Sorellae,R.C.Terinf, H. C. Toledog Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Maracanã, Rio de Janeiro 20550-013, Brazil Received: 9 March 2018 / Accepted: 11 September 2018 © The Author(s) 2018 Abstract We construct a vector gauge invariant transverse due to the high energy behavior of the longitudinal vector field configuration V H , consisting of the well-known super- degree of freedom. In the abelian case it is perfectly compen- field V and of a Stueckelberg-like chiral superfield .The sated by the dynamics of the Stueckelberg field but in non- renormalizability of the Super Yang Mills action in the Lan- abelian theories this seems to be not so, resulting in incur- dau gauge is analyzed in the presence of a gauge invariant able divergent interacting amplitudes or unbounded cross mass term m2 dVM(V H ), with M(V H ) a power series sections. in V H . Unlike the original Stueckelberg action, the resulting Nevertheless there have been recent interests in the study action turns out to be renormalizable to all orders. of massive vector models without the Higgs. The main moti- vation comes here from the continuous efforts to understand the low energy behavior of strongly interacting gauge the- 1 Introduction ories, such as QCD. Confinement is a very important phe- nomenon in this context, but the physical mechanism behind In this work we study the renormalizability properties of a it is still an open problem. A way to obtain information about N = 1 non-abelian gauge theory defined by a multiplet con- this phenomenon is through lattice investigations which have taining a massive vectorial excitation. The model we study revealed that the gluon propagator shows a massive behav- is the supersymmetric version of a Stueckelberg-like action, ior in the deep infrared non-perturbative region, while also in the sense that the massive gauge field is constructed by displaying positivity violations which precludes a proper par- means of a compensating scalar field, thus preserving gauge ticle propagation interpretation [7–13]. Therefore, in a con- invariance. fining theory, the issue of the physical unitarity is a quite The history of Stueckelberg-like models is very well complex and difficult topic. Of course, physical unitarity reviewed in [1]. Traditionally, most of the investigations must hold in terms of the physical excitations of the spec- have studied such models as potential alternative to the trum which are bound states of quarks and gluons like, for Higgs mechanism of mass generation, but as discussed in instance, mesons, barions, glueballs, etc. Though, the posi- [2] there seems to be an unavoidable clash between renor- tivity violation of the two-point gluon correlation functions malizability and unitarity in non-abelian Stueckelberg-like is taken as a strong evidence of confinement, signalling that models. The original Stueckelberg model is abelian and has gluons are not excitations of the physical spectrum of the been rigorously proved [3] to be renormalizable and uni- theory. Nevertheless, renormalizability should be expected tary, but its non-abelian version is known to be perturba- to hold since one wants to recover the good UV behavior of tively non-renormalizable [4–6]. Physically, the problem is QCD. This trend of investigations led to many works that pro- posed modifications of the Yang-Mills theory to accommo- a e-mail: [email protected] date the lattice results [14–18]. Recent developments along b e-mail: [email protected] these lines involve the introduction of modified Stueckelberg- c e-mail: [email protected] like models [19–23] constructed as a generalization of a class d e-mail: [email protected] of confining effective theories known as Gribov–Zwanziger e e-mail: [email protected] scenarios [24,25], see [26] for a review. Unlike the stan- f e-mail: [email protected] dard Stueckelberg action, these modified models enjoy the g e-mail: [email protected] pleasant property of being renormalizable to all orders, see 0123456789().: V,-vol 123 797 Page 2 of 14 Eur. Phys. J. C (2018) 78:797 [19–23] for a detailed account on the construction of these 2PureN = 1 SUSY Stueckelberg-like Yang–Mills modified models and on their differences with the standard theory Stueckelberg theory. Let us also also mention here that, recently, a BRST invariant reformulation of the Gribov– In order to define the N = 1 Supersymmetric Stueckelberg- Zwanziger theory has been achieved [21,23], allowing its like Yang–Mills theory, we start with a real abelian gauge extension from the Landau gauge to an arbitrary covariant superfield, gauge. The present model is intended only to construct a renor- μ i V (x,θ,θ) = C + iθχ − iθχ + θσ θ Aμ + θθ(M + iN) malizable theory which generalizes the non-supersymmetric 2 construction given in [22]. Issues like the perturbative uni- i i μ − θθ(M − iN) + iθθ θ¯ λ¯ + σ¯ ∂μχ tarity of the models so obtained are not explicitly addressed. 2 2 As far as we know, the non-supersymmetric model is not per- i μ − iθθθ λ − σ ∂μχ turbative unitary. Though, it can be successfully employed 2 as an effective renormalizable model in order to investigate 1 1 the non-perturbative infrared region of confining Yang–Mills + θθθθ D − ∂2C , (1) theories. So far, the prediction of the non-supersymmetric 2 2 model are in good agreement with the actual lattice data on and with a massless chiral superfield that acts as a Stueckel- the correlation functions of the theory, like the two-point berg field gluon propagator. Our aim here is to construct a sypersimmetric generaliza- √ ( ,θ,θ) = ξ( ) + θψ( ) + θσμθ∂¯ ξ( ) − θθ ( ) tion of this model for a future investigation of the confine- x x 2 x i μ x f x ment aspects of pure STM, which is known to be a confining i μ ¯ 1 2 − √ θθ∂μψ(x)σ θ − θθθθ∂ ξ(x) (2) theory. This is the main purpose of the present model. 4 2 √ μ In a confining YM theory, the issue of the unitarity has (x,θ,θ) = ξ(x) + 2θψ(x) − iθσ θ∂μξ(x) to be faced through the study of suitable colorless bound- i μ state, a topic which is still too far from the goal of the present − θθ f (x) + √ θθθσ ∂μψ(x) work, whose aim is that of obtaining a renormalizable mas- 2 1 sive SPYM theory which generalizes the model of [22]. − θθθθ∂2ξ(x). (3) In this work we will carry out a supersymmetric general- 4 ization of the Stueckelberg-like model proposed in [19–23]. It is then possible to construct a gauge-invariant superfield We prove that the present supersymmetric generalization is renormalizable, a task that will be done by means of a set of H ( ,θ,θ) = ( ,θ,θ)+ ( ,θ,θ)− ( ,θ,θ), suitable Ward identities. Supersymmetric generalizations of V x V x i x i x (4) Stueckelberg-like models was studied since very early [27] but mostly concentrated on the better behaved abelian mod- which is invariant under the abelian gauge transformations els (see [28–30], for instance, for a proposal of an abelian Stueckelberg sector in MSSM), with some constructions of V → V + iφ − iφ, → − φ, → − φ. (5) non-abelian theories with tensor multiplets [31–33] and also with composite gauge fields [34]. We now need a generalization of the definition of V H to the The work is organized as follows. In Sect. 2 we con- non-abelian case. We start with the gauge-invariant superfield struct the N = 1 Supersymmetric massive classical action. (4) with every component now in the adjoint representation In Sect. 3 we discuss the gauge fixing and the ensuing BRST of the gauge group G, V H ≡ V HaT a, (a = 1,...,dim G) symmetry. Sections 4 and 5 are devoted to the derivation where the T a are the generators in the adjoint. Now, the H of a set of suitable Ward identities and to the characteri- fundamental object is eV instead of V H . The non-abelian zation of the most general invariant local counterterm fol- generalization of (4)is lowing the setup of the algebraic renormalization. In Sect. 6 we provide a detailed analysis of the counterterm by H eV = HeV H, (6) showing that it can be reabsorbed into the starting classi- cal action through a redefinition of the fields and parame- = i = iφ ters, thus establishing the all orders renormalizability of the where H e , U e and V is a usual gauge superfield. model. Section 7 contains our conclusion. The final Appen- The gauge transformations then have to be dices collect the conventions and a few additional technical − −1 details. eV → UeV U, H → U 1 H, H → H U , (7) 123 Eur. Phys. J. C (2018) 78:797 Page 3 of 14 797 such that V H is gauge invariant. For infinitesimal transfor- 3 Supersymmetric gauge invariant Stueckelberg-like mations, this explicitly yields Yang–Mills action in the Landau gauge i i The supersymmetric extension of the Landau gauge is [1] δgaugeV = L V (φ + φ) + (L V coth(L V/ ))(φ − φ) 2 2 2 2 i i D D2V = 0. (14) = i(φ − φ) + [V,φ+ φ]+ [V, [V,φ− φ]] 2 12 +O(V 3), (8) We thus need to add the following terms to the action δ = i φ − 1( ( ))φ gauge L L cot L/2 1 2 2 2 2 LSGF = Tr dSAD D V + c.c.
Load more

Recommended publications
  • Redalyc.A Local Non-Abelian Gauge Invariant Action Stemming from The
    Brazilian Journal of Physics ISSN: 0103-9733 [email protected] Sociedade Brasileira de Física Brasil Dudal, D.; Capri, M. A. L.; Gracey, J. A.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Verschelde, H. A Local Non-Abelian Gauge Invariant Action Stemming from the Nonlocal Operator F(D2)-1F Brazilian Journal of Physics, vol. 37, núm. 1B, march, 2007, pp. 232-238 Sociedade Brasileira de Física Sâo Paulo, Brasil Available in: http://www.redalyc.org/articulo.oa?id=46437212 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative 232 Brazilian Journal of Physics, vol. 37, no. 1B, March, 2007 A Local Non-Abelian Gauge Invariant Action Stemming from the 2 ¡1 Nonlocal Operator Fµn(D ) Fµn D. Dudala,¤ M. A. L. Caprib, J. A. Graceyc, V. E. R. Lemesb, R. F. Sobreirob, S. P. Sorellab,† and H. Verscheldea a Ghent University Department of Mathematical Physics and Astronomy, Krijgslaan 281-S9, B-9000 Gent, Belgium b UERJ - Universidade do Estado do Rio de Janeiro, Rua Sao˜ Francisco Xavier 524, 20550-013 Maracana,˜ Rio de Janeiro, Brazil c Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, P.O. Box 147, Liverpool, L69 3BX, United Kingdom (Received on 12 September, 2006) 2 ¡1 We report on the nonlocal gauge invariant operator of dimension two, Fµn(D ) Fµn. We are able to localize this operator by introducing a suitable set of (anti)commuting antisymmetric tensor fields.
    [Show full text]
  • Jhep11(2016)024
    Published for SISSA by Springer Received: June 27, 2016 Revised: September 1, 2016 Accepted: October 16, 2016 Published: November 7, 2016 Massless and massive higher spins from anti-de Sitter space waveguide JHEP11(2016)024 Seungho Gwak,a Jaewon Kima and Soo-Jong Reya;b aSchool of Physics and Astronomy & Center for Theoretical Physics, Seoul National University, Seoul 08826, Korea bFields, Gravity & Strings, Center for Theoretical Physics of the Universe, Institute for Basic Sciences, Daejeon 34047, Korea E-mail: [email protected] Abstract: Understanding Higgs mechanism for higher-spin gauge fields is an outstanding open problem. We investigate this problem in the context of Kaluza-Klein compactifica- tion. Starting from a free massless higher-spin field in (d + 2)-dimensional anti-de Sitter space and compactifying over a finite angular wedge, we obtain an infinite tower of heavy, light and massless higher-spin fields in (d + 1)-dimensional anti-de Sitter space. All mas- sive higher-spin fields are described gauge invariantly in terms of Stueckelberg fields. The spectrum depends on the boundary conditions imposed at both ends of the wedges. We ob- served that higher-derivative boundary condition is inevitable for spin greater than three. For some higher-derivative boundary conditions, equivalently, spectrum-dependent bound- ary conditions, we get a non-unitary representation of partially-massless higher-spin fields of varying depth. We present intuitive picture which higher-derivative boundary conditions yield non-unitary system in terms of boundary action. We argue that isotropic Lifshitz in- terfaces in O(N) Heisenberg magnet or O(N) Gross-Neveu model provides the holographic dual conformal field theory and propose experimental test of (inverse) Higgs mechanism for massive and partially massless higher-spin fields.
    [Show full text]
  • Universality of the Chern-Simons Diffusion Rate
    PHYSICAL REVIEW D 98, 106023 (2018) Universality of the Chern-Simons diffusion rate † ‡ Francesco Bigazzi,1,* Aldo L. Cotrone,1,2, and Flavio Porri1,2, 1INFN, Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino (Firenze), Italy 2Dipartimento di Fisica e Astronomia, Universit`a di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino (Firenze), Italy (Received 20 August 2018; published 27 November 2018) We prove the universality of the Chern-Simons diffusion rate—a crucial observable for the chiral magnetic effect—in a large class of planar strongly correlated gauge theories with dual string description. When the effects of anomalies are suppressed, the diffusion rate is simply given in terms of temperature, entropy density and gauge coupling, with a universal numerical coefficient. We show that this result holds, in fact, for all the top-down holographic models where the calculation has been performed in the past, even in the presence of magnetic fields and anisotropy. We also extend the check to further well-known models for which the same computation was lacking. Finally we point out some subtleties related to the definition of the Chern-Simons diffusion rate in the presence of anomalies. In this case, the usual definition of the rate—a late time limit of the imaginary part of the retarded correlator of the topological charge density—would give an exactly vanishing result, due to its relation with a nonconserved charge correlator. We confirm this observation by explicit holographic computations on generic isotropic black hole backgrounds. Nevertheless, a nontrivial Chern- Simons relaxation time can in principle be extracted from a quasinormal mode calculation.
    [Show full text]
  • Broken Symmetries and Transport in Holography
    Broken Symmetries and Transport in Holography Memoria de Tesis Doctoral realizada por Amadeo Jim´enez presentada ante el Departamento de F´ısicaTe´orica de la Universidad Aut´onomade Madrid para optar al T´ıtulode Doctor en F´ısicaTe´orica Tesis Doctoral dirigida por Karl Landsteiner, Investigador del Instituto de F´ısicaTe´oricaUAM/CSIC Departamento de F´ısicaTe´orica Universidad Aut´onomade Madrid Instituto de F´ısicaTe´orica UAM/CSIC Marzo de 2015 Agradecimientos Por suerte tengo mucho que agradecer. En primer lugar quiero expresar mi gratitud a Karl, que ha iluminado mi odisea a trav´esde la ocuridad hologr´afica. Por su infinita paciencia y su buen humor. Por estar siempre dispuesto a discutir y ayudarme a comprender. Realmente ha sido un placer y un honor. Gracias por ponerme en el camino en el que estoy. He tenido la suerte de coincidir con Luis, mi \hermano" de tesis, a lo largo de este viaje. Gracias por explicarme tantas cosas. Estoy convencido de que no hubiera llegado hasta aqu´ısin tu ayuda. No olvidar´elas conversaciones de f´ısicay de no f´ısicacon Dani, Diego, Javi, Jo~ao, Mateo y Pablo d´ıatras d´ıa.Ojal´ase repitan. Querr´ıatambien mencionar a algunos profesores con los que he tenido la oportunidad de conversar y que me han iluminado e inspirado especialmente: Ho-Ung, Ioannis y Pepe. No me olvido de mis amigos de siempre: Bad´ıa, Blanco, Charlie, Hector, Jaime, Juan y Tupi. Con vosotros la vida es mejor. Hay un lugar especial aqu´ıpara Irene, el gusano que me ha acompa~nadoy soportado en esta maravillosa etapa de mi vida.
    [Show full text]
  • Ext-2004-043.Pdf
    The Charge-Mass-Spin Relation of Clifford Polyparticles, Kerr-Newman Black Holes and the Fine Structure Constant Carlos Castro Center for Theoretical Studies of Physical Systems Clark Atlanta University, Atlanta, GA. 30314 A Clifford-algebraic interpretation is proposed of the charge, mass, spin relationship found recently by Cooperstock and Faraoini which was based on the Kerr-Newman metric solutions of the Einstein-Maxwell equations. The components of the polymomentum associated with a Clifford polyparticle in four dimensions provide for such a charge, mass, spin relationship without the problems encountered in Kaluza-Klein com- pactifications which furnish an unphysically large value for the electron charge. A physical reasoning behind such charge, mass, spin relationship is provided, followed by a discussion on the geometrical derivation of the fine structure constant by Wyler, Smith, Gonzalez-Martin and Smilga. To finalize, the renormalization of electric charge is discussed and some remarks are made pertaining the modifications of the charge-scale relationship, when the spin of the polyparticle changes with scale, that may cast some light into the alleged Astrophysical variations of the fine structure constant. EXT-2004-043 01/09/2003 Key words : Clifford Algebras; Black Holes; Dirac electron. PACS : 11 E88, 15 A66, 83 C57 1. INTRODUCTION 1.1 CLIFFORD ALGEBRAS IN PHYSICS Clifford algebras display a rich mathematical structure which is very useful for a unified description of geometry and physics [1,2,3,4,5,6,9]. For example, a geometric approach to the physics of the Standard Model in terms of Clifford algebras was advanced by [3] . Important applications have also been found in string theory, extended objects, gravity, QFT...
    [Show full text]
  • Massive Gravity from Double Copy
    Published for SISSA by Springer Received: April 28, 2020 Revised: September 6, 2020 Accepted: October 27, 2020 Published: December 4, 2020 Massive gravity from double copy JHEP12(2020)030 Arshia Momeni,a Justinas Rumbutisa and Andrew J. Tolleya,b aTheoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2AZ, U.K. bCERCA, Department of Physics, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106, U.S.A. E-mail: [email protected], [email protected], [email protected] Abstract: We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions 2 1/3 are consistent with a Λ3 = (m MPl) cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory.
    [Show full text]
  • Gauge Fields and Fermions in Tachyon Effective Field Theories
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server hep-th/0011226 CTP-MIT-3044 UUITP-11/00 Gauge Fields and Fermions in Tachyon Effective Field Theories Joseph A. Minahan1 Department of Theoretical Physics Box 803, SE-751 08 Uppsala, Sweden and Barton Zwiebach2 Center for Theoretical Physics Massachusetts Institute of Technology Cambridge, MA 02139, USA Abstract In this paper we incorporate gauge fields into the tachyon field theory models for un- stable D-branes in bosonic and in Type II string theories. The chosen couplings yield massless gauge fields and an infinite set of equally spaced massive gauge fields on codi- mension one branes. A lack of a continuum spectrum is taken as evidence that the stable tachyon vacuum does not support conventional gauge excitations. For the bosonic string model we find two possible solvable couplings, one closely related to Born-Infeld forms and the other allowing a detailed comparison to the open string modes on bosonic D-branes. We also show how to include fermions in the type II model. They localize correctly on stable codimension one branes resulting in bose-fermi degeneracy at the massless level. Finally, we establish the solvability of a large class of models that include kinetic terms with more than two derivatives. 1E-mail: [email protected] 2E-mail: [email protected] 1 Contents 1 Introduction and summary 2 2 Coupling gauge fields to the superstring tachyon model 6 2.1Thesuperstringmodelrevisited........................ 6 2.2Couplingtogaugefields............................ 8 3 Coupling gauge fields to the bosonic string tachyon model 11 3.1Thebosonicstringmodelrevisited.....................
    [Show full text]
  • Renormalizability of Super Yang–Mills Theory in Landau Gauge with A
    Eur. Phys. J. C (2018) 78:797 https://doi.org/10.1140/epjc/s10052-018-6239-5 Regular Article - Theoretical Physics Renormalizability of N = 1 super Yang–Mills theory in Landau gauge with a Stueckelberg-like field M. A. L. Capria, D. M. van Egmondb, M. S. Guimaraesc, O. Holandad, S. P. Sorellae,R.C.Terinf, H. C. Toledog Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Maracanã, Rio de Janeiro 20550-013, Brazil Received: 9 March 2018 / Accepted: 11 September 2018 / Published online: 1 October 2018 © The Author(s) 2018 Abstract We construct a vector gauge invariant transverse due to the high energy behavior of the longitudinal vector field configuration V H , consisting of the well-known super- degree of freedom. In the abelian case it is perfectly compen- field V and of a Stueckelberg-like chiral superfield .The sated by the dynamics of the Stueckelberg field but in non- renormalizability of the Super Yang Mills action in the Lan- abelian theories this seems to be not so, resulting in incur- dau gauge is analyzed in the presence of a gauge invariant able divergent interacting amplitudes or unbounded cross mass term m2 dVM(V H ), with M(V H ) a power series sections. in V H . Unlike the original Stueckelberg action, the resulting Nevertheless there have been recent interests in the study action turns out to be renormalizable to all orders. of massive vector models without the Higgs. The main moti- vation comes here from the continuous efforts to understand the low energy behavior of strongly interacting gauge the- 1 Introduction ories, such as QCD.
    [Show full text]
  • Theoretical Exercises 2016 Contents
    November 30, 2016 Theoretical Exercises 2016 Thomas Becher Albert Einstein Center for Fundamental Physics Institute for Theoretical Physics University of Bern Contents 1 Gaussian integrals and Wick's theorem 1 1.1 Gaussian integrals . .1 1.2 Generating function, Wick's theorem . .2 2 Integrals over Grassmann variables 4 3 Dirac Algebra 6 3.1 Levi-Civita symbol . .6 3.2 Dirac Algebra . .8 4 Klein-Gordon, Maxwell and Proca equations 11 4.1 Klein Gordon equation . 11 4.2 Electromagnetic field in relativistic notation . 11 4.3 Proca equation . 12 4.4 Gauge invariance . 13 5 Spinors and Dirac equation 15 5.1 Lorentz transformation of spinor fields . 15 5.2 Dirac Lagrangian and Dirac equation . 19 5.3 Plane-wave solutions . 19 6 Non-relativistic limit of the Dirac equation 22 6.1 Dirac equation in the presence of an electromagnetic field . 22 6.2 Magnetic moment of the electron . 23 7 Interacting fields in perturbation theory 25 7.1 Relativistically invariant interaction Lagrangians . 25 7.2 Perturbation theory . 27 7.3 Wick's theorem . 28 7.4 Feynman rules . 30 7.4.1 φ4-theory . 30 7.4.2 QED . 31 7.4.3 QED with an extra neutral scalar S .................... 32 8 Computation of scattering cross sections 33 8.1 Reduction formula and S-matrix . 33 8.2 Cross section and decay rate . 35 9 Diphoton production and a scalar resonance 37 9.1 Decays of the scalar S ............................... 38 9.2 Diphoton production . 39 9.3 Finite-width effects . 41 9.4 Data analysis . 42 2 1 Gaussian integrals and Wick's theorem 1.1 Gaussian integrals Exercise 1.1.
    [Show full text]
  • Massive Born-Infeld and Other Dual Pairs Abstract: S
    Published for SISSA by Springer Received: February 9, 2015 Accepted: March 6, 2015 Published: April 8, 2015 Massive Born-Infeld and other dual pairs JHEP04(2015)032 S. Ferraraa,b,1 and A. Sagnottia,c aDepartment of Physics, CERN Theory Division, Geneva 23, CH-1211 Switzerland bINFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, Frascati, I-00044 Italy cScuola Normale Superiore and INFN, Piazza dei Cavalieri 7, Pisa, I-56126 Italy E-mail: [email protected], [email protected] Abstract: We consider massive dual pairs of p-forms and (D p 1)-forms described − − by non-linear Lagrangians, where non-linear curvature terms in one theory translate into non-linear mass-like terms in the dual theory. In particular, for D = 2p and p even the two non-linear structures coincide when the non-linear massless theory is self-dual. This state of affairs finds a natural realization in the four-dimensional massive N = 1 supersymmetric Born-Infeld action, which describes either a massive vector multiplet or a massive linear (tensor) multiplet with a Born-Infeld mass-like term. These systems should play a role for the massive gravitino multiplet obtained from a partial super-Higgs in N = 2 Supergravity. Keywords: Supersymmetry and Duality, Supersymmetry Breaking, Duality in Gauge Field Theories ArXiv ePrint: 1502.01650 1On leave of absence from Department of Physics and Astronomy, U.C.L.A., Los Angeles, CA, U.S.A. Open Access, c The Authors. doi:10.1007/JHEP04(2015)032 Article funded by SCOAP3. Contents 1 Introduction 1 2 Massless and massive dualities 2 3 Self-dualities in even dimensions 5 4 Self-dual massive dualities in odd dimensions 7 JHEP04(2015)032 5 N = 1 superspace formulation 8 6 Massive supersymmetric Born-Infeld and its superspace dual 10 7 Discussion 11 A The dual massive Born-Infeld-like action 11 1 Introduction Non-linear theories of p-form gauge fields naturally arise in Superstrings and are clearly relevant in the description of brane dynamics as models for the partial breaking of Su- persymmetry.
    [Show full text]
  • Renormalizability of $\Mathcal {N}= 1$ Super Yang-Mills Theory In
    RENORMALIZABILITY OF =1 SUPER YANG-MILLS THEORY IN LANDAU GAUGE WITHN A STUECKELBERG-LIKE FIELD 1M. A. L. Capri,∗ 1D.M. van Egmond,† 1M. S. Guimaraes,‡ 1O. Holanda,§ 1S. P. Sorella,¶ 1R. C. Terin,∗∗ and 1H. C. Toledo†† 1Departamento de F´ısica Te´orica, Rua S˜ao Francisco Xavier 524, Universidade do Estado do Rio de Janeiro, 20550-013, Maracan˜a, Rio de Janeiro, Rio de Janeiro, Brazil. H We construct a vector gauge invariant transverse field configuration V , consisting of the well- known superfield V and of a Stueckelberg-like chiral superfield Ξ. The renormalizability of the Super Yang Mills action in the Landau gauge is analyzed in the presence of a gauge invariant mass term 2 H H H m R dV M(V ), with M(V ) a power series in V . Unlike the original Stueckelberg action, the resulting action turns out to be renormalizable to all orders. I. INTRODUCTION In this work we study the renormalizability properties of a = 1 non-abelian gauge theory defined by a multiplet containing a massive vectorial excitation. The model we studyN is the supersymmetric version of a Stueckelberg-like action, in the sense that the massive gauge field is constructed by means of a compensating scalar field, thus preserving gauge invariance. The history of Stueckelberg-like models is very well reviewed in [1]. Traditionally, most of the investigations have studied such models as potential alternative to the Higgs mechanism of mass generation, but as discussed in [2] there seems to be an unavoidable clash between renormalizability and unitarity in non-abelian Stueckelberg-like models.
    [Show full text]
  • Arxiv:Hep-Th/0011226V1 24 Nov 2000 Ial,W Sals H Ovblt Falrecaso Oesta Include That Models of C Class Localize Derivatives
    hep-th/0011226 CTP-MIT-3044 UUITP-11/00 Gauge Fields and Fermions in Tachyon Effective Field Theories Joseph A. Minahan1 Department of Theoretical Physics Box 803, SE-751 08 Uppsala, Sweden and Barton Zwiebach2 Center for Theoretical Physics Massachusetts Institute of Technology Cambridge, MA 02139, USA Abstract In this paper we incorporate gauge fields into the tachyon field theory models for un- stable D-branes in bosonic and in Type II string theories. The chosen couplings yield massless gauge fields and an infinite set of equally spaced massive gauge fields on codi- mension one branes. A lack of a continuum spectrum is taken as evidence that the stable arXiv:hep-th/0011226v1 24 Nov 2000 tachyon vacuum does not support conventional gauge excitations. For the bosonic string model we find two possible solvable couplings, one closely related to Born-Infeld forms and the other allowing a detailed comparison to the open string modes on bosonic D-branes. We also show how to include fermions in the type II model. They localize correctly on stable codimension one branes resulting in bose-fermi degeneracy at the massless level. Finally, we establish the solvability of a large class of models that include kinetic terms with more than two derivatives. 1E-mail: [email protected] 2 E-mail: [email protected] 1 Contents 1 Introduction and summary 2 2 Coupling gauge fields to the superstring tachyon model 6 2.1 Thesuperstringmodelrevisited . 7 2.2 Couplingtogaugefields ............................ 8 3 Coupling gauge fields to the bosonic string tachyon model 11 3.1 The bosonic string model revisited .
    [Show full text]