Teorie supersimmetriche con deformazione di Leigh-Strassler e modelli matriciali
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(271) GW F;9;TV [S_E@` ?;TF [9]K` SFGW H %[ H2` > 2` 9xw 0 TX"^ ?;9W%[ SSFW&Y-Y<`aW9]K`a^-]^ ?GW F;SF^<VX]^< V 9` F@` ?;T>29 %[ 9`$` VM[PY-Y-GW F]WGY-WPV >a^ 1W ?J?:^ F;<d%[ 6-`aWPV` 0 O [ aT` OV %[ 9 [ > [ 9^-GW F` []^<`|_BW&]:^ >2> `|_G%[ 9;F`aY<` %[ > ` P^-B] p [ 9;FW <P%[ 9W%[ SS> `aY\%[ 6-`aWPVX^O` V _BGW >29`%[ >29;F`Y\[(Z_ S` G9;F [nn` aT %[ > `Kn` ?@` ?;9^<_E`K]K@` ?GW F]K` V %[ 9`X^ > [ 9^-GW F` []:^ >2> [Y-WPZ_ S>a"^ ?J?2` 9xw 0 QzAV 9;T9;9`;`®Y\G[ ?f` ?` 9;F %[ 9;9 []K`&GW 9;9^<VX:^ F^ TV []K@` ?;9;F2` HT6-`aWPVX^T]K`&%[ T9#W <d%[ >aGW F`&_B^-]K` [(VX]W ?;T TV ` V ?`a^<_B^T]K`|_G%[ 9;F`aY<` 0 QR>?JTXY-Y-"^ ?J?W]Kf` aTX"^ ?;9`®_BW;]:^ >2> ` 3]#W <fT9Wn[(VXxY pX^T%[ >_ %[ 9;9WJY pX^ "^ ?@` ?;9WPVXW % )M) !& ) !# 0 g3%[ >a^ TV m[ ?GW F;9 []K ` 9^-GW F^<_G[ ]:^ >t> ` _E2` 9^Y-^< V 9;F %[ >a1^ [ aT [(VX]mW >a^]K` _B^<V ?`aWPV`$]:^ >2> [_G%[ 9;F`aY-^ ¬W _B:^ K1> `aW 2` >
(272) V T_B:^ FWG]K ` <d%[ F` %[ H2` > `R%[ >a^\%[ 9GW F`a^ ` VX]K2` S1^<VX]^< V 9` Z]K2` <|^<V 9 [ K1F [(VX]^ > [ ]K@` ?;9;F2` HT6-`aWPVX^ ]:^ K1> `%[ T9#W <d%[ >aGW F` 9^<VX]^ [P
(273) ] TV [ ]K@` ?;9;F2` HT6-`aWPVX^ > ` _E2` 9^ &JY pX^nVXWPVS]K2` S
(274) ^<VX]^]X[(`1]:^ 9;9 %[ K1> `1]:^ >2> [ _E@` ?;TF [ ]Kv` SFGW H %[ H2` > 2` 9xw ` V2` 6-` %[ >a^_G[ ]X%[ >2>a^ SFGW SF`a:^ 9xw]Kv` ?` _E_B:^ 9;F` []:^ >2> 4 ` V ?`a^<_B^ 0 TX"^ ?;9 [Y-WPV K|:^ 9;9;TF [ VXWPV ]K`$_GY\[(G[ f` ?'`?J9 S %[ %[ 9 F;[9`a]KY-` GW _B> %[ 1W F?;` 9;0 F %[ 9 [` CV K|^<VX:^ F %[ >a^ P_G[ ?;9 %[ 9 [ <|:^ F` P Y\%[ 9 [` V TV [ K1F [(VX]-^ <P%[ F`a:^ 9xw U >29;F` ?:^ 9;9GW F`]K`X%[ SS> `aY\%[ 6-`aWPVX^]:^ >2>a^¸_G%[ 9;F`aY<` %[ >a^\%[ 9GW F`a^ ?WPVXW > [ % O P`K_BW;]:^ >2> ` ?;9 %[ 9@` ?;9`aY<`Ob O ?JT F:^ 9`aY-GW > `T%[ >a^\%[ 9GW F` '> [ 9^-GW F` [/]:^ >2>aZ^ ?;9;F` V K1pX^Em^ > [ NMuf 9^-GW F` [ 0 V [ . . . . . . . . .
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(276) /10 eZN>W&]^:>2> `_G[%9;F`aY<` [%> `. /1/. ]^"?Y:F`26-`aWPVX^ ]^<` _BW&]^:>2> ` _G[%9;F`aY<` [%> `VX^:>2> [U>aWGFW K|^<VX^:F [%> `29xwUST /^"?J? ^:F^C9;FW <P[%9 [S` V ^o / c /1/ R0 ° ° ¥ T£Cª Xªz§R£O¥ O¥ ² § O¥ ²g²´§ V_BW&]:^ >2>aWE_G%[ 9;F`aY<` [%>a^ ]^8PXV`29WG]X[ V K1F;TSS
(277) WB]K` ?` _E_B:^ 9;F` [ G • VB` V ?`a^<_B^]K`X_G%[ 9;F`aY<` Y-WPV TV [q_E@` ?;TF [ dM ®^<V9;F [(_ H`` V <P[%F` [(V 9` ? WG9;9W • 2` >IK1F;TSS1WG]KI` ?` _E_B:^ 9;F` [ E 1?GW > 2` 9 [(_B^<V 9^¸VX^:>2> [ _ WGF_G[ H
(278) WG>29;6-_G[(VV` [(V [ V [ >a:^ K1K|^CY-]KWPf` ZV SFTGW V H %[S
(279) HGW 2` 9> ^<2` 9xV w 6-`P(M • ) %[ >a^ |^-]E:^ <|^<V9;T [%> _B^<V 9^ TV`29 [[%>2> [_E`@?;TF [ e ` V _¬GW F_Gm[ K®%[ TK|^?f´` V <P%[ F` [( V 9^ 0 V(M ) %TWP_BC^ SF"^ ?:Y F2` 9;9WG]X%[ >2> [GY-WPV K|:^ 9;9;TF [B]K` O ` cWd K1F [d[ _@uf g3[ _´ [ Y-WPV ?`a]:^ F:^ F^<_BW ?^<_ f SF^ > 4 ` V ?`a^<_B^ ]:^ >2>a^ _G%[ 9;F`aY<` pX:^ F_E2` 9` [(VX^ Y-WPV>2` >*K1F;TSS
(280) WS]K` ?` _E_B:^ 9;F` [ U (N ) 0 QgV a TX"^ ?;9WEY\G[ ?ZW > [_E@` ?JTF [ BaTX:^ >2> [B]K` [d%[ F . . . . . −N 2 V(M ). dM =. N Y. dMii. Y. d <e Mij d =m Mij. TX^"?;9 [E_E`@?;TF [ q` V<d[%F` [(V9^ ? WG9;9WZ9;F [G?W_ WGF_G[%6-`aWPV`TV`29 [%F`a^ i=1. i<j. Y-WPV U U = 1 W1?J?` [(_BW aT` VX]K`$]K` [%K|WPV [%> `26"6[%F^ > [_G[%9;F`aY-^ApX^:F_E`29` [(V [ M Y-WPV Λ = ]K` %[ K (λ , . . . , λ ) M = U ΛU ^-] ^"?;SF` _B^:F^ K1> ` N ]K` 7^:F^<V6-` [%> `Z]K` dM %[ 9;9;F "[ <|:^ FJ? \W K1> ` N ]K` 7^:F^<V6-` [%> `¸]^:K1> ` [%T9W <P[%>aWGF` dΛ ^ZK1> ` N − N ]K` 7:^ F^<V 6-` %[ > -` F` _G[(VX^< V 9` dU 0 %C` "BY-WP_BW&]W S
(281) WP` f Yxp Z> [ >a^:K1K|^E]K`SFWGH [%H`2> 2` 9xw ` V <d%[ F` [(V 9^ ?GW 9;9W/2` > K1F;TSS1WM]K` ?` _E_B:^ 9;F` [ U (N ) a T` VX]K`t> 4 ` V9^:K1F [%6-`aWPVX^` V dU ]K2` <|^< V 9 m[ H [(V %[ >a^q^ F"^ ?J92` 9;T@` ?Y-^2` > <|GW >2T_B^q]:^ >tK1F;TSS
(282) W Y-WP_ZS [%9;9W 0 Ql>
(283) Y\[(C_ H`aW ]K`1Y-W&GW F]K` V %[ 9^q` V 9;FW&n] TXY-^ S1:^ F VX:^ >2> 4 ` V 9:^ K1F %[ >aA^ TVXW c[PY-GW H` [7f VXW J 05O %[ 9 m[ > 4 ` V <d%[ F` [(V 6[B]:^ >2> [ _E@` ?JTF [ aTX"^ ?J9W ST B"^ ?J?:^ F^ _´[PY<2` > _B^<V 9^ Y\%[ >aY-GW > %[ 9W VX:^ >2> 4 ` V 9GW FVXWS]K` U = 0 QzV ]8^ PXV2` 92` <d[EGW 9;9^<V` [(_BW Y /10 b dM = (λ − λ ) dΛdU 3 Z[ >a:^ K1K|^ ]K'` SFGW H %[ H2` > 2` 9xw Y-WP_BA^ SF"^ ?:Y F2` 9;9W <&`a^<VX^`a]^<V 9` P Y\%[ 9 [GY-WPV M → U †M U. †. †. 1. N. 2. 2.
(284) . . i. j. . 2. i<j. ]W <|^. P(M ) = e−N Tr W (M ). W (M ) =. n+1 X k=1. gk k M k. ]^:K. W = n+1. .
(285) /b. ER^-WGF`a^. N =1. haTX>aWZ^"?;?;9 9[m^"?J>a^:?K1WmK|S
(286) ^ WG]K9`'^<VS6-F` WG[%H >a^ [%H]`2^:> `2>29x> [w9q^-WG` V F<P` [Z[%Fa ` [(T V [P9]n^CF` ?fzWG]K9;` 9_BWE^<`2V>'?K1`aWPF;TV S[%>aS
(287) ^WB[G]K?x?`IW;?Y<` _E` [%_B9 [ ^:0 9;V;F` `[ VX0 WG9`$YJpX^ V [ ]^:>2>a^ a T [(V9`29xw YJpX^ S
(288) W1?J?WPVXW ^"?J?^:F^^"?;9;F [%9;9^]X[%>_BW&]^:>2>aWq ^YJpX ^ UF> ` [ f ?;T>29^:Fxw` _ZS
(289) WGF;9 [(V9^ S
(290) ^:FC>aW ?;9;TX]K`aWM]^:> > ` _E`29^ R 9^:F_BW&]K` V [(_E`aY-W ]K`@?;9;F`2HT6-`aWPVX^ ]^:K1> ` [%T9W <P[%>aWGF` X]^8PXV`29 [ N →∞. ρ(λ). ρ(λ) =. N 1 1 X hδ(λ − λi )i = hTr δ(λ − M )i N N. ] W#<|^`2>'<d[%>aWGF_B^-]K`aW Y\[%>aY-WG> [%9WSY-WPV > [m>a^:K1K|^ ]K`ISFWGH [%H`2> `29xw ^h> [E]K`@?;9;F`2HT6-`aWPVX^ F`@?;T>29 [VXWGF_G[%> `26"6[%9 [S[ 1 0 ° ° 7² ¥µd§ O§ 3ªC£Rµd§©¦(¥ ²z²z¢ QR> S1GW 9^<V 6-` %[ >a^S8^ 7
(291) :^ 9;92` <|W ^ a T` VX]K` 9;T9;9^U>a^ aT [(V 9`29xwM]K`C` V9^:F^"?J? ^GY\[%>aY-WG> [%H`2> ` %[ 9;9;F "[ <|:^ FJ?ZW > [Y-WPV K|:^ 9;9;TF [G]K` O ` cWd K1F [d[ _@uf g3[_´[ nS1W1?J? WPVXW^"?x?^:F^^"?;9;F [%9;9`$]X[%>2> 4 ^<VX^:Ff Kd` C[ > 2` H
(292) :^ F []:^ >
(293) _BW;]:^ >2>aW _G%[ 9;F`aY<` %[ >a^VX:^ >t> ` _E2` 9^]Kt` K1F [(VX]^ N m[ ?;T [ <|GW >29 []8^ PXV2` 9 [ %[ 9;9;F "[ <|:^ FJ?UW > [ _TV 6-`aWPVX^ ]K` S %[ F;92` 6-`aWPVX^ i=1. . . Z=e. −N 2 F. =. Z. dM e−N Tr W (M ). WP`axY p nY<` ` V9^:F^"?J? [ Y\[%>aY-WG> [%F^ > 4 ` V 9^:K1F [%>a^ ? WG>aWVX^:>> ` _E`29^]K`K1F [(VX]^ ®[%SS> ` f YJpX^:F^<_BW TV 4 [%SSFW1?x?` _G[%6-`aWPVX^]K`'STV 9WU?^:>2> [ 0 S1^:F` [(_BWE`2> Y\[(_CH`aWG]K`N<P[%F` [%H`2> ` /10 b ¸^q` V9^:K1F` [(_BWG`2>I<|WG>2T_B^ ]^:>IK1F;TSS
(294) WB]K`'K®[%TK|^1[
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