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supersymmetric yang - mills quantum mechanics ( symqm ) provides the quantitative model of m - theory @xcite . even though much simpler than the original theory the model is not solved in spite of its long history@xcite . we have therefore decided to set up a systematic lattice survey of symqm beginning with the simplest case of @xmath1(quenched)@xcite and gradually extending it as far as possible towards the bfss limit _ i.e. _ @xmath2 and @xmath3 . in this talk i will report on the second step along this programme : the first results for higher n will be presented . the action of the symqm reads @xmath4 where @xmath5 , and all fields are independent of the space coordinates @xmath6 . the supersymmetric fermionic partners belong to the addjoint representation of su(n ) . the discretized system is put on a @xmath7 dimensional hypercubic lattice @xmath8 which is reduced in all space directions to @xmath9 , @xmath10 . the gauge part of the action has now the usual form s_g=-_m=1^n_t _ > 1n re ( u_(m ) ) , [ sg ] with = 2n / a^3 g^2 , [ beta ] and @xmath11 , @xmath12 , where @xmath13 denotes the lattice constant and @xmath14 is the gauge coupling in one dimension . the integer time coordinate along the lattice is @xmath15 . periodic boundary conditions @xmath16 , @xmath17 , guarantee that wilson plaquettes @xmath18 tend , in the classical continuum limit , to the appropriate components @xmath19 without the space derivatives . up to date we have addressed the two problems : 1 ) extracting the continuum limit from the lattice data , and 2 ) the search for the nontrivial phase structure . the first point is essential in any approach based on the discretization . in particular restoration of the continuum supersymmetry , of the full unquenched model , may crucially depend on the ability to control the continuum limit . the second issue is connected to the problem of the bekenstein - hawking entropy which has an elegant solution in the framework of m - theory @xcite . namely the supersymmetric , extremal black holes found in the latter can be viewed as composed of the elementary d0 brane excitations , providing the statistical interpretation of the area of the `` schwarzschild '' horizon which is known to behave as an etropy . in particular , the theory also predicts existence of the two phases in which the gravity and the elementary d0 branes provide good description respectively@xcite . we have found in @xcite that the continuum limit of the model can be readily extracted with the bare parameters scaling with canonical dimensions . this is expected for the one dimensional system . to search for the phase transition we have studied the distribution of the eigenvalues of the polyakov line @xmath20 , which is a very sensitive determinant of the phase structure in gauge theories . it was found that , similarly to the large volume qcd , in the low temperature phase the eigenvalues are concentrated around zero , while at high temperature the distribution is peaked around @xmath21 which constitute the center of su(2 ) . in the space extended theories the @xmath22 symmetry is spontaneously broken in the infinite volume limit and only one direction is populated . in the present 0-volume system , this may happen only in the infinite - n limit , the gross - witten model being a known example of the critical behaviour emerging at large n. for higher groups we find now the same behaviour , see fig.1 . since @xmath23 , the histograms correspond to the low and high temperature regions for a range of @xmath24 . evidently they change from convex to concave at some critical value of @xmath25 similary to the n=2 case . the nature of the transition is not resolved yet . nevertheless , our data show unambiguously that the system behaves differently in both regions . for example , we have also measured the dependence of the size of the system , @xmath26 , on the temperature , and found that it is definitely different , and the change in the behaviour occurs at the same t where the distributions in fig . 1 change their shapes . it is also possible , for the first time to confront the n dependence of the transition temperature with theoretical expectations . it follows from eq.([beta ] ) and @xmath27 , that the t hooft scaling @xmath28 implies that the lattice coupling @xmath29 at fixed @xmath30 . fig.2 shows the @xmath24 dependence of @xmath31 for available range of n together with the fit of the first @xmath32 correction . indeed , the reduced critical coupling seems to saturate towards higher n and one can estimate that @xmath33 result is within @xmath34 15% of the @xmath35 one ( a horizontal line ) . we have also studied the new , noncompact formulation of the model which has better numerical behaviour @xcite . in this approach the @xmath36 spatial degrees of freedom are noncompact @xmath37 and are defined at the discrete time intervals , while the temporal one remains compact @xmath38 . the action @xmath39 reads @xmath40 the covariant finite difference along the time direction @xmath41 takes into account the parallel transport between adjacent lattice sites . this system has the same local gauge invariance as the compact version , eq.([sg ] ) . with the new action we have extended previous study to higher dimensions , d=6 and d=10 . preliminary simulations confirm results found for d=4 . in particular the average size of the system @xmath42 shows a characteristic break in the temperature dependence at the position consistent with the t hooft scaling . moreover , the @xmath42 decreases with d in agreement with the mean field results @xcite . quantitative lattice study of the yang - mills quantum mechanics , and possibly the m - theory , have just begun . quenched results are encouraging , but a lot remains to be done . simulations work for all interesting values of the dimension @xmath7 and are feasible for a range of n. recent results give us a rough idea how the large n limit is approached and where the asymptotics sets it . all quenched simulations performed up do date indicate existence of the two regions at finite temperature . this intriguing correspondence with the predictions of the m - theory should be further quantified . of course , the next step is to include the dynamical fermions . this can be done by a brute force for d=4 and for the first few n s at d=10 . the one dimensional nature of the system should help considerably . for higher n , at d=10 , we face the problem of the complex pfaffian . an important insight into the whole subject may be gained by applying the full potential of the small volume approach @xcite . 9 t. banks , w. fishler , s. shenker and l. susskind , . m. claudson and m. b. halpern , . u. h. danielsson , g. ferretti and b. sundborg , . m. b. halpern and c. schwartz , . r. a. janik and j. wosiek , ; hep - lat/0011031 . a. strominger and c. vafa , . e. j. martinec , hep - th/9909049 . p. bialas and j. wosiek , hep - lat/0109031 . d. kabat , g. lifszytz and d. a. lowe , . m. lscher , ; p. van baal , ; p. van baal , hep - ph/0008206 .
we present new results of the quenched simulations of the reduced d=4 supersymmetric yang - mills quantum mechanics for larger gauge groups su(n ) , @xmath0 . 
 the model , studied at finite temperature , reveals existence of the two distinct regions which may be precursors of a black hole and the elementary d0 branes phases of m - theory conjectured in the literature . 
 present results for higher groups confirm the picture found already for n=2 . 
 similar behaviour is observed in the preliminary simulations for the d=6 and d=10 models .