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AdS5 S5 SU(N) N = 4 N = 4 gS R2/ R AdS5 S5 N g = g2 N YM YM 4 R2 = gS, =. N AdS5 S5 |OA A OA = Tr(i i... i ) (i)ab 1 2 n N = 4 SU(N) N N E MA,B R2 OA(x) OB(y) = HString|OA =EA, gS |OA 1 N (x - y)2 A(, ) 1 R2 ! , = E, gS N P SU(2, 2|4) OA(x) |OA gS = 0 AdS5 S5 N AdS5 S5 AdS5 S5 1 1 AdS5 S5 N J S5 J J2/N n2 n = J + 2 1 + J2 /J2 J AdS5 S5 N = 4 Y N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 N = 4 // N = 4 // N = 4 // N = 4 // N = 4 // // N = 4 // N = 1 N = 2 N = 4 // N = 4 // N = 4 // // N = 4 // // // N = 4 // N = 4 // N = 4 N = 4 0() = -4g2 - + 1 + - 2 (1), 2 2 j 1 (0) uni(j + 2) = -8 g2S1(j) = -8 g2 = -8 g2 (j + 1) - (1). k k=1 N = 4 j j m m sgn(a) sgn(a) Sa(m) =, Sa,b,c,...(m) = Sb,c,...(j). ja ja j=1 j=1 N = 4 |a| + |b| + |c| +... N = 4 CA = CF = N Tf = 2N N = 4 Sa,b,... = Sa,b,...(j) (1) uni(j + 2) = 16 S1 S2 + S-2 + 8 S3 + 8 S-3 - 16 S-2,1, N = 4 N = 4 1 + (-1)j-k (2k + 1) S1(j) - S1(k) ND(1) uni j,k = 4 (k - 1)4 (j - k)(j + k + 1) j - k j + k S1 - 2S1(j - k) - S1 (j - 1)4 + (k - 1)4 2 2 + 2(j - 1)4 S1(j) + 2(k - 1)4 S1(k), (a)k = (a + k)/(a) CA CF Tf CA = CF = N Tf = 2N N SU(N) N = 4 N = 4 N = 4 N = 4 M = -1 + 4 6 -4 g2 -4 g2 -4 g2 = 2 - 4 3 + O. M = -1 + M M M 170 M = -1 + S-7 S7 M = -1+ 1/7 S7 = 1/7 ABA 8 = 256 (4 S-7 + 6 S7) + 186 terms. S-7 S7 N = 4 N = 4 Y M Y M OK = tr eg V Ie-g V I, g =, 4 2 = gY M N OK = tr ii = tr AiAi + BiBi, i = 1, 2, 3, i Ai Bi 130 000 4-loop K,pl = 12 g2 - 48 g4 + 336 g6 + - 2496 + 576 3 - 1440 5 g8 5 5 5 uni(j + 2) = - 640 S1(j) 5. (3) 5 1/N2 d44 d44 = N2(N2 + 36)/24, K = 12g2 -48g4 +336g6+ -2496 + 576 3 - 1440 1 + 5 g8, N 5 np = 0, M= 48 gnp = -360 5 + O g10, M=N 25 48 gnp = 21 + 70 3 - 250 5 + O g10. M=9 N 5 uni(j + 2) = - 640 S1(j) 1 + 5. (3) N 5 5 5 3 (3) uni,np, 5(j + 2) = - 160 S1(j), (3) uni,np, 3(j + 2) = -192 S1(j) S1(j) S-2(j) + S3(j), (3) (3) (3) (3) uni,np(j)= uni,np, (j) 5 + uni,np, (j) 3 + uni,np,rat(j). 5 N N = 4 N = 4 N = 4 N = 4 725 000 S F F d i ab mF (L) = -m cosh (Sab( + ) - 1)e-mL cosh , 2 - b ab Sab() L c ab ab m(L) = - (m2 - |m2 - m2|)c (-i) Sab() e- L. a b c ab b,c E2 = m2 + p2 E2 = 1 + 8g2 sin2 p N = 4 4-loop = 324 + 8643 - 14405 g8. wrapping M sl(2) M = -1 + 1 500 1 500 N N N + j Si,...,ik(N) = (-1)N (-1)j Si,...,ik(j), 1 j j j= M M M M = -1 + N = 4 N = 4 N = 4 N = 4
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