22 Pages·2012·2.92 MB·English

Non-abelian dyons in anti-de Sitter space Elizabeth Winstanley Consortium for Fundamental Physics School of Mathematics and Statistics University of Sheﬃeld United Kingdom Work done in collaboration with Ben Shepherd ElizabethWinstanley (Sheﬃeld) Non-abeliandyonsinanti-deSitterspace BritGrav12,April2012 1/13 Outline 1 A brief history of Einstein-Yang-Mills 2 su(N) EYM with Λ < 0 3 Dyonic solutions 4 Conclusions and outlook ElizabethWinstanley (Sheﬃeld) Non-abeliandyonsinanti-deSitterspace BritGrav12,April2012 2/13 Introduction A brief history of Einstein-Yang-Mills Asymptotically ﬂat EYM studied for over 20 years Purely magnetic su(2) solitons and black holes found numerically 1989-90 Have no magnetic charge Non-abelian baldness of asymptotically ﬂat su(2) EYM If Λ = 0, the only solution of the su(2) EYM equations with a non-zero (electric or magnetic) charge is Abelian Reissner-Nordstr¨om Rules out dyonic su(2) asymptotically ﬂat solutions [ Ershov and Gal’tsov, PLA 138 160 (1989), 150 159 (1990) ] Ershov/Gal’tsov result no longer holds for larger gauge group in asymptotically ﬂat space What about asymptotically anti-de Sitter space? ElizabethWinstanley (Sheﬃeld) Non-abeliandyonsinanti-deSitterspace BritGrav12,April2012 3/13 Introduction A brief history of Einstein-Yang-Mills Asymptotically ﬂat EYM studied for over 20 years Purely magnetic su(2) solitons and black holes found numerically 1989-90 Have no magnetic charge Non-abelian baldness of asymptotically ﬂat su(2) EYM If Λ = 0, the only solution of the su(2) EYM equations with a non-zero (electric or magnetic) charge is Abelian Reissner-Nordstr¨om Rules out dyonic su(2) asymptotically ﬂat solutions [ Ershov and Gal’tsov, PLA 138 160 (1989), 150 159 (1990) ] Ershov/Gal’tsov result no longer holds for larger gauge group in asymptotically ﬂat space What about asymptotically anti-de Sitter space? ElizabethWinstanley (Sheﬃeld) Non-abeliandyonsinanti-deSitterspace BritGrav12,April2012 3/13 Introduction A brief history of Einstein-Yang-Mills Asymptotically ﬂat EYM studied for over 20 years Purely magnetic su(2) solitons and black holes found numerically 1989-90 Have no magnetic charge Non-abelian baldness of asymptotically ﬂat su(2) EYM If Λ = 0, the only solution of the su(2) EYM equations with a non-zero (electric or magnetic) charge is Abelian Reissner-Nordstr¨om Rules out dyonic su(2) asymptotically ﬂat solutions [ Ershov and Gal’tsov, PLA 138 160 (1989), 150 159 (1990) ] Ershov/Gal’tsov result no longer holds for larger gauge group in asymptotically ﬂat space What about asymptotically anti-de Sitter space? ElizabethWinstanley (Sheﬃeld) Non-abeliandyonsinanti-deSitterspace BritGrav12,April2012 3/13 Introduction A brief history of Einstein-Yang-Mills Asymptotically ﬂat EYM studied for over 20 years Purely magnetic su(2) solitons and black holes found numerically 1989-90 Have no magnetic charge Non-abelian baldness of asymptotically ﬂat su(2) EYM If Λ = 0, the only solution of the su(2) EYM equations with a non-zero (electric or magnetic) charge is Abelian Reissner-Nordstr¨om Rules out dyonic su(2) asymptotically ﬂat solutions [ Ershov and Gal’tsov, PLA 138 160 (1989), 150 159 (1990) ] Ershov/Gal’tsov result no longer holds for larger gauge group in asymptotically ﬂat space What about asymptotically anti-de Sitter space? ElizabethWinstanley (Sheﬃeld) Non-abeliandyonsinanti-deSitterspace BritGrav12,April2012 3/13 Introduction A brief history of Einstein-Yang-Mills Asymptotically ﬂat EYM studied for over 20 years Purely magnetic su(2) solitons and black holes found numerically 1989-90 Have no magnetic charge Non-abelian baldness of asymptotically ﬂat su(2) EYM If Λ = 0, the only solution of the su(2) EYM equations with a non-zero (electric or magnetic) charge is Abelian Reissner-Nordstr¨om Rules out dyonic su(2) asymptotically ﬂat solutions [ Ershov and Gal’tsov, PLA 138 160 (1989), 150 159 (1990) ] Ershov/Gal’tsov result no longer holds for larger gauge group in asymptotically ﬂat space What about asymptotically anti-de Sitter space? ElizabethWinstanley (Sheﬃeld) Non-abeliandyonsinanti-deSitterspace BritGrav12,April2012 3/13 su(N)EYMwithΛ<0 The model for su(N) EYM Einstein-Yang-Mills theory with su(N) gauge group 1 (cid:90) √ S = d4x −g[R −2Λ−TrF Fµν] µν 2 Field equations 1 R − Rg +Λg = T µν µν µν µν 2 D Fµ = ∇ Fµ+[A ,Fµ] = 0 µ ν µ ν µ ν Stress-energy tensor 1 T = TrF Fλ− g TrF Fλσ µν µλ ν 4 µν λσ ElizabethWinstanley (Sheﬃeld) Non-abeliandyonsinanti-deSitterspace BritGrav12,April2012 4/13 su(N)EYMwithΛ<0 Static, spherically symmetric, conﬁgurations Metric ds2 = −µ(r)σ(r)2dt2+[µ(r)]−1dr2+r2(cid:0)dθ2+sin2θdφ2(cid:1) 2m(r) Λr2 µ(r) = 1− − r 3 su(N) gauge potential [ Kunzle Class. Quant. Grav. 8 2283 (1991) ] Static, dyonic, gauge potential 1 (cid:16) (cid:17) i (cid:104)(cid:16) (cid:17) (cid:105) A dxµ = Adt + C −CH dθ− C +CH sinθ+Dcosθ dφ µ 2 2 N −1 electric gauge ﬁeld functions h (r) in matrix A j N −1 magnetic gauge ﬁeld functions ω (r) in matrix C j ElizabethWinstanley (Sheﬃeld) Non-abeliandyonsinanti-deSitterspace BritGrav12,April2012 5/13 su(N)EYMwithΛ<0 Static, spherically symmetric, conﬁgurations Metric ds2 = −µ(r)σ(r)2dt2+[µ(r)]−1dr2+r2(cid:0)dθ2+sin2θdφ2(cid:1) 2m(r) Λr2 µ(r) = 1− − r 3 su(N) gauge potential [ Kunzle Class. Quant. Grav. 8 2283 (1991) ] Static, dyonic, gauge potential 1 (cid:16) (cid:17) i (cid:104)(cid:16) (cid:17) (cid:105) A dxµ = Adt + C −CH dθ− C +CH sinθ+Dcosθ dφ µ 2 2 N −1 electric gauge ﬁeld functions h (r) in matrix A j N −1 magnetic gauge ﬁeld functions ω (r) in matrix C j ElizabethWinstanley (Sheﬃeld) Non-abeliandyonsinanti-deSitterspace BritGrav12,April2012 5/13

Non-abelian dyons in anti-de Sitter space Elizabeth Winstanley Consortium for Fundamental Physics School of Mathematics and Statistics University of She eld

Upgrade Premium

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.